Surfaces Gemcom

5/20/2018 Surfaces Gemcom

1/128

Page 3143

Modelling Chapter 8: Surfaces

Chapter 8

Surfaces

In This Chapter

Introduction

Surface Features Using Surfaces

Creating Surfaces

Intersecting Surfaces

Contouring Surfaces

Displaying Surfaces

Surface Volume Reporting

Creating a SEGfor Block Model Interfacing

IntroductionIn Gemcom, surfaces can represent several types of topographic

information including:

Original topographies

As-mined topographies

Pit designs Dump layouts

Sub-surface structures such as geological structures, faults or

lithological contacts.

In Gemcom, you can create surface models using a triangulated

irregular network (TIN), and then display and manipulate the models.


2/128

Page 3144

Section III: Solids Modelling and Evaluation Gemcom for Windows

Surface Features

Triangulated surfaces have many characteristics that differentiate

them from other computerized surface models:

Each data input point will be used as a vertex of at least one

triangle, so the surface always exactly honours the input data.

All polylines representing distinct surface features, such as toe

and crest lines (known as breaklines), will be honoured in the TIN.

Triangles will be as close to equilateral as possible while still

maintaining edge integrity.

The boundary of the surface will be a convex polygon that

encompasses all input points.

The surface will not have any holes in it, unless a clipping

operation is performed after initial surface creation.

As triangulated surfaces generally provide the best possible surface

representation of topographical data, they have many uses in mining

operations.

Surface Creation Data Elements

There are three data elements used to create and modify surfaces:

3Ddata points, called nodes

3Dline segments connecting two nodes, called edges

2Dpolygons that can be used to remove parts of a surface that fallinside or outside their boundaries, called clipping polygons.


3/128

Page 3145


Using Surfaces

In Gemcom, you can:

Create surfaces from combinations of active drillhole intersects,

points and polylines.

Intersect surfaces with other surfaces or solids.

Contour surfaces to create new polylines.

Create surface elevation grids from surfaces.

Each of the above applications is described more fully in this chapter.

For instructions on the performing the above procedures, see Chapter

12: The Surface Menu.

Creating Surfaces

Gemcom lets you create surfaces using active data consisting of

discrete points (such as drillhole intersects, spot heights, or sample

locations) and polylines representing breaks in slope (such as surface

contours, bench crest lines, or bench toe lines). These surfaces are

created as a series of connected triangular panels, also known as a

triangulated irregular network (TIN). The surface is able to preserve

all the breaks in the feature lines used to make the TIN. A TINsurface

gives the best approximation of surfaces for subsequent operations

such as volume calculations.

You can also create surfaces using the Laplace gridding method.

Creating TIN Surfaces

The triangulation process can operate in either theXYplane (in plan),

which is the most common method for modelling topographic data; or

in a local plane fitted through the data, which is the best way toaccurately model sub-surface, near vertical, or overturned structures

(see Figure 8-1).


4/128

Page 3146


Forcing TIN Edges

Gemcom can preserve edges (polyline segments) during the creation of

a TINin order to give the best possible representation of the surface.

This can, however, cause problems if the polylines cross and there isan elevation conflict at the intersection point. If you are making a

surface that includes polylines, it is recommended that you check for

crossing edges and correct them using the polyline editing functions

before proceeding with the surface creation.

Figure 8-1: A surface created in theXYplane (top) and an

overturned surface created in a best fit plane


5/128

Page 3147


TIN Boundary Trimming

Gemcom will, by default, make a surface whose perimeter is theconvex limits of all data points used in its creation. There are times

when this results in unsightly (and incorrect) surfaces, especially

around the edges (see Figure 8-2). In addition to the surface/polygon

clipping commands, you can specify a maximum edge length for the

boundary of the TIN. In many cases, this will automatically remove

these long boundary triangles and give a more realistic surface. Be

careful not to make this number too small, as too many TINedges maybe removed and the TINwill be unusable.

Validation of Surfaces

Gemcom provides the capability for validating surfaces upon creation

(or upon importation into Gemcom). Although construction errors withsurfaces are far less common than with solids, it is generally a good

idea to validate surfaces as well.

Each edge in a valid surface is either part of two triangles, in the case

of interior edges, or part of only one triangle, in the case of edges along

the perimeter. Also, a triangle in a valid surface may not intersect any

other triangles. When a surface is validated, Gemcom checks for self-intersecting triangles and for triangle edges connected to more edges

than allowed.

Without TIN boundary trimming With TIN boundary trimming

Figure 8-2: Effect of TINboundary trimming on concave perimeter


6/128

Page 3148


If problems are discovered, the relevant areas are highlighted so that

you can correct the surface. Gemcom lets you save the bad areas of the

surface to assist visually in the correction of the surface errors.

Laplace Gridding

Laplace gridding provides a very fast and effective way to create

gridded surfaces in any orientation to represent any of the following:

Topographic surfaces (for example, created from drillhole collars or

survey data)

Faults (created from specific contact points on drillholes)

Tops and bottoms of seams (again using drillhole interval data)

Grade values on a specific plane (typically created using the realvalue component of extraction point data)

Features

The main features of using Laplace gridding are as follows:

Gridding can be done on any plan. Grids on plan views, vertical

sections, and inclined sections can be handled with equal ease.

Different types of data can be used when making a single grid (for

example, drillhole collars, contours, and control stations can all be

used together to make a grid of surface topography).

All the data used for the gridding process can be visually checkedfor correctness, both in 2Dand 3D.

The process is graphical so the results of the gridding can be seen

immediately, both in 2Dand 3D.

The results can be saved in a number of different formats, allowing

the results to be used by other Gemcom systems.


7/128

Page 3149


There is no size limit to the grid; the amount of data used for

gridding and the size of the grid itself is limited only by available

memory.

Data Points

Laplace gridding allows you to create a grid on the current view plane

using the same active data points as other surface creation commands,

including:

Points (extraction points or control stations)

Polylines (usually status lines such as toes, crests, contours)

Drillhole points (collars or interval points)

Storage Formats

Once the Laplace grid interpolation is complete, the grid can be savedin a number of different formats:

Gemcom standard *.MEXextraction file

ASCII status map file containing polylines along rows of the grid

PC-MINE ASCII surface grid file

Surface TIN

The grid can be saved to a surface that can be contoured, clipped with

other surfaces or solids, plotted, etc.

Advantages

Laplace gridding has a number of advantages over other interpolationmethods (such as inverse distance and kriging):

Robust, in that a grid will be produced regardless of the input data,

unless data values exist in all grid cells or there are no data points

in any grid cells.

There is no logical limit on the number of input data points. In

excess of 80,000 data points have been successfully interpolated.


8/128

Page 3150


The method is not particularly sensitive to the distribution of

input points. Lines or clusters of points do not give rise to any

special problems.

The time taken to create a grid does not depend significantly upon

the number of input data points. It can even turn out that the run

time for creating the grid will decrease as the number of points is

increased. Run times from a few minutes to a maximum of around

two hours can be expected.

The grid has a smooth appearance and produces smooth lookingcontours. (This may not always be an advantage, depending upon

the nature of the input data.)

The degree of smoothing (bi-cubic spline) is userspecified.

One disadvantage, however, is that the accuracy of the resulting grid

cannot (as far as we know) be quantified in statistical terms. You must

study the resulting grid visually and subjectively to decide whether

you are happy with its appearance.

Laplace Gridded Surfaces Versus TINs

Gemcom provides two distinct methods of creating surfaces from point

data, namely Laplace gridding and surface creation from TINs. Eachmethod has its advantages.

Laplace gridded surfaces Surface creation from TINs

Pros Easily set up to coincidewith block model or seammodel.

Effectively fills in areas ofsparse or missing data.

Preserves the original points.

Cons Original data points usuallynot preserved in final grid.

Yields poor results when data pointsare dispersed and/or irregularlydistributed. Large triangles will becreated.


9/128

Page 3151


Laplace Gridded Surfaces

Laplace gridding will form a grid (with user-defined size and location)

and each cell of the grid will be assigned a value (typically anelevation or grade value) based on the distribution and proximity of

known data points. The iterative method processes all cells, updating

the values each time until eventually a smooth gridded surface has

been created.

Laplace gridding generally does not honour the original data points.

For example, if you made a grid using drillhole collars, it is likely thatmany of the grid cells will be either slightly higher or lower than the

drillhole collar points used in their creation (due to the averaging and

smoothing of the Laplace technique). This may pose problems when

the drillholes and resulting Laplace grid surface are shown together

(for example, if you cut a section through the data) as the drillholes

collars will not exactly coincide with the surface. This may pose even a

bigger problem when modelling faults using drillhole intervals, wherethe preservation of the exact 3Dpoints defining the fault are very

important.

Surface Creation from TINS

TINs are formed by creating triangular panels that connect knownpoints and/or polylines. Only known points are used in the TIN

creation; there is no interpolation of new points with this method.

Thus, sparse or missing data can lead to problems.

For example, if you have only a few hundred drillholes and you want

to make a surface representing the topography of the property,

creating a surface using TINs may not give a satisfactory result. TINswork best when there is a high concentration of points to give

adequate control and to keep the triangular panels to a relatively

small size (for example, making a surface of a pit design). TINs will

generally be attractive for working with surveyed stockpiles or open

pits and design quality open pit models.


10/128

Page 3152


Combined Method

Gemcom provides a third alternative. By combining the TINand

Laplace gridding methods to create a single surface, the strengths ofboth can be used while eliminating the drawbacks of using either

independently. The process is as follows:

1. Activate the data points that will be used for creating the grid.

2. Create a Laplace grid that covers the area of interest and grid it.

3. Save the results to an extraction file.

4. Load the extraction file along with the original data points.

5. Create a surface using the TINmethod.

This process will first "fill in" the sparse areas with points from the

Laplace gridding method, then create a TINusing both the interpolatedpoints andthe original data points. Both objectives are achieved; the

surface honours the known data points exactly while still providing a

smooth, natural representation of the whole surface by incorporating

the interpolated points.

General Procedure

Follow these steps to create a Laplace gridded surface:

1. Activate the data points to be used for the gridding process.

Depending on the type of surface you are creating, this may

include any combination of drillhole, point, or polyline data.

To use extraction file data:

Choose Point }}Data }}Load Data from Extraction File. Select

the name of the file containing the desired data to use for the grid

from the File Name dialog box that appears and choose OK.

In the editor that appears, enter the display parameters. If you are

displaying location values, select the Elevation field as yourdisplay field. If you are displaying grade values, select either the


11/128

Page 3153


Real or Integer field as your display field. See Volume I: Core for

more information.

To use drillhole data:

Choose Drillhole }}Data }}Load Drillholes. From the picklists

that appear, select the desired loading and display profiles and

records.

Use the Drillhole }}Selectsubmenu to activate all (or part) of the

data that you want to use. See Volume II: Explorationfor more

information.

To use polyline data:

Choose Polyline }}Data }}Load Polylines from Status Map.

See Volume I: Core for more information.

2. Laplace gridding occurs relative to the current view plane.Determine the orientation you want your grid to follow by

selectingView }}Vertical Section, Inclined Sectionor Plan

View. You must select a plane to activate the desired orientation,

although which plane you choose is not important, as the plane

itself is not needed by the application. For more information on

selecting planes, see Volume I: Core.

3. Change the current viewing mode to 2D.

For manual gridding, this step is optional, but may help you to

define the grid parameters, which must be specified in 2Dplanar

coordinates. Decide on the extents and parameters for the grid,

considering such factors as the distance between original data

points, the total number of original data points, and the final levelof density of data required. If you are also working with a surface

elevation grid, you will likely want to coordinate the size of the

Laplace grid with that of the SEG.

4. Choose Surface }}Create }}Create Surface by Laplace

Gridding }}Define Grid Location Manuallyor Define Grid

Location Graphically and follow the command proceduresdescribed in Chapter 12: The Surface Menu.


12/128

Page 3154


Laplace Gridding Process

The Laplace gridding method is very simple in concept. Gemcom

solves a set of finite difference equations in an iterative manner. Theequation being solved is

( )[ ] 2 2 4 4 0+ + =y C y z

where C = Smoothing factor.

If C = 0, then no smoothing will occur. The grid will try to join datapoints with straight lines. As C is increased, more smoothing is

introduced, with the grid tending towards a bi-cubic spline function.

Gemcom uses the following sequence to generate the grid:

1. Read in data and allocate to nearest grid cell.

2. Where data was derived from digitized polygon data, insert extra

points automatically along the polygon line if the digitized points

are too far apart. Use the integer value of records in the extract

file to decide whether points belong to the same polygon. Exclude

points more than one cell width from the boundary of the surface

grid.

3. Set grid cell to average of all data values in the grid cells which

contain more than one data point.

At this point, processing of input data ceases. Only processing of the

grid itself occurs in the following steps.

4. Set all unknown grid cells either equal to the closest known grid

cell or to the average of all known grid cells.

5. Solve the finite difference equations iteratively, with the unknown

grid cells being progressively adjusted to satisfy the above

equation (to a limit of 999 iterations).

The rate of convergence depends upon the amount of smoothing

used and the distribution of initial data points. The maximumnumber of iterations, the iteration acceleration factor and the


13/128

Page 3155


threshold for convergence have been preset to avoid any possible

user confusion.

Copying Surfaces

You can create a new surface by copying and renaming an existing

surface. The new surface will contain the same attribute information

as the original. This command can be used to make a temporary

backup copy of any surface prior to performing editing operations.

As this command lets you enterX,Y, and/or Zoffset values, you can

copy and move a surface in one step. This is useful in cases where you

want to make a solid from the surface for evaluation purposes. For

example, if you have a surface that represents the top of a five-metre-

thick seam , you can copy the top surface with an offset of -5 meters,

thus creating the bottom of the seam. You can then mesh the two

surfaces together to create a solid.

Creating a Surface From Two Surfaces Using MathFunctions

You can create a new surface by applying a mathematical function totwo existing surfaces. The available functions are plus, minus, divide,

multiply, minimum, maximum, and average. The function operates on

the Zvalues of the two surfaces, and, in concert with an optional scale

factor and constant, yields the Zvalues of the resulting surface

according to this equation:

Zresult = Scale Factor Function(Ztop, Zbottom) + Constant

Each node on the top surface is projected onto the "bottom" surface to

calculate the new Zvalues according to the equation. The new surface

will contain the same number of nodes as thefirstsurface selected in

this operation, and not the cumulative points of both surfaces as may

be expected. Therefore, the top surface should have corresponding

nodes on the bottom surface. For this reason, we suggest that thiscommand be used with surfaces created by the Laplace Gridding

Application and having exactly the same dimensions andXYlocations.


14/128

Page 3156


This command works relative to the current view plane, so it can

operate on horizontal, vertical, and inclined surfaces.

Intersecting Surfaces

Gemcom lets you perform several advanced merging/clipping

operations using surfaces. For example, you can clip all polylines or

solids above or below a surface, select or deselect points above or below

a surface, or merge surfaces together to make a new surface. This lastcapability is useful in cases where you have one surface representing

topography and another representing a pit design, and you wish to

combine them.

As shown in Figure 8-3, you can:

Create the polyline of intersection between two surfaces.

Clip the portion of one surface that lies above a second,

intersecting surface.

Clip the portion of one surface that lies below a second,

intersecting surface.

Create the minimum, or the maximum, of two intersectingsurfaces.

Create the solid formed by two completely intersecting surfaces.

By using theViewmenu commands with a limited corridor width, you

can quickly view the top surface/plane intersection using surface

models. These intersections can be used for plotting or as referencesfor on-screen digitizing in conjunction with block model/drillhole/point

information.


15/128

Page 3157


Figure 8-3: Two intersecting surfaces, cut away to show detail (top)

and the minimum of the two surfaces on left


16/128

Page 3158


Contouring Surfaces

You can contour any surface to create new polylines. Contouring

involves slicing surfaces with sets of parallel planes. Contour lines arethe polylines of intersection between the surface being contoured and

the parallel planes (see Figure 8-4). Contour lines are stored as

polylines; once created, they can be edited, smoothed, manipulated or

used in the same way as any other polylines. Contouring can be done

in global or local view coordinates at specified intervals.

You can define the planes in six ways:

Contour in 3Dglobal coordinates. This method contours

the selected solids/surfaces using horizontal planes. You must

specify the upper and lower elevation ranges (defined in global

coordinates) and a contouring interval. For example, if you

enter 100 as the upper elevation and 0 as the lower elevation

with a 25 metre interval, you will get contours at 5 elevations,namely 100, 75, 50, 25, and 0 metres.

Contour in 2Dview coordinates. This method contours the

selected solids/surfaces using planes parallel to the current

view plane, allowing you to contour in any orientation. You

must enter a towards distance for contouring (the positive

distance in front of the view plane), an away distance (thepositive distance behind the view plane), and a contour

interval. For example, if you enter 15 as the towards distance

and 10 as the away distance with a 5 metre interval, you will

get contours on 6 different planes, these being 15, 10, and 5

metres in front of the active view plane, the active view plane

itself (0 distance), and 5 and 10 metres behind the view plane.

Contour current view plane only. This method uses the

current view plane for contouring. No towards or away

distances are required.


17/128

Page 3159


Figure 8-4: Contours created on a set of plan views (top)

and a set of vertical sections

Contour all active vertical sections. This method contoursthe solids/surfaces using all active vertical sections. The actual

planes used for contouring are obtained from the vertical

section profiles active in the current Gemcom session. You can

select vertical sections using Polyline }}Select }}Select

Vertical Sections.

Contour all active inclined sections.This method contoursthe solids/surfaces using all active inclined sections. The actual

planes used for contouring are obtained from the inclined

P 3160


18/128

Page 3160


section profiles active in the current Gemcom session. You can

select inclined sections using Polyline }}Select }}Select

Inclined Sections.

Contour all active plan views. This method contours the

solids/surfaces using all active plan views. The actual planes

used for contouring are obtained from the plan view profiles

active in the current Gemcom session. You can select plan

views using Polyline }}Select }}Select Plan Views.

Gemcom is very flexible in that you can contour several solids and/or

surfaces at once. In addition, solids need not be of the same classyou

can contour Geology, Excavation, and Surface class solids in the same

operation.

Assigning Plane Attributes

If you contour a Geology class solid, the resulting polylines will be 3D

Rings that require a plane and rock code attribute. If you contour an

Excavation or Surface class solid, the resulting polylines will be Status

Lines that require a plane and line type attribute. There are two ways

to assign the plane attribute:

Automatically from plane. This command tells Gemcom to usethe plane elevation (if contouring using the 3DGlobal coordinates

option) or the distance from the view plane (if contouring using the

2DView coordinates option) as the plane attribute of all new

polylines. For example, if a polyline was created by intersecting a

solid with a plane at elevation 3860, activating this option would

assign 3860 as the polylines plane attribute. This option should

only be used in cases where you have planes defined with thesenames. If you are contouring using predefined planes (Vertical

sections, Inclined sections, or Plan views) activating this option

will assign the plane attribute of all new polylines to the name of

the plane currently being processed.

Based on default plane.The plane attribute for all polylines will

be set to a user-specified default value.

Page 3161


19/128

Page 3161


Surfaces with Identical Areas

Intersection operations with surfaces require a line of intersection. If

the two surfaces have large areas which are identical, the line ofintersection will include all edges in those areas. With such a long line

of intersection, processing time and the need for available memory

greatly increases. However, temporarily shifting one of the surfaces a

small amount (such as 2mm in elevation) will usually resolve the

problem.

Fixing Invalid Surfaces After Intersection

The intersection of surfaces requires complex computations for many

of the triangles which make up the surfaces. In isolated instances, the

newly created surface may have triangles with extreme properties

which render it invalid. However, temporarily shifting one of thesurfaces a small amount (such as 2mm in elevation) will usually

resolve the problem.

Page 3162


20/128

Page 3162


Displaying Surfaces

Each TINcreated within Gemcom (or imported into Gemcom) belongs

to one of three classes: Geology, Excavation or Surface. Each activeTINis displayed based on its class assignment. You can define different

display parametersfor each classat any time. These parameters

include:

Solid display mode. You can choose one of two modes for

displaying the TIN:

Solid fillshows the TINwith solid coloured panels (whenviewed in rendered mode).

Wireframeshows only the TINedges and no panels.

Obtain colour from. Gemcom can use one of three methods to

assign a colour to each individual triangle within the TIN:

Primary colourmethod colours all triangles the same,according to the colour assigned to the TINwhen it is created.

Triangle dipmethod colours each triangle based on its dipangle (in degrees). This option is very useful in cases where thetriangle dip values are critical, for example, in pit design orslope stability work. Gemcom can provide a very fast graphicaloverview of the slopes of your entire TIN.

Triangle Zmethod colours each triangle based on the Zvalueof the triangle centroid.

Colour profile for display. The Triangle Dip and Triangle Z

display options require a colour profile to be defined that provides

colours for all possible value ranges. It is generally wise to definecolour profiles specifically for TINviewing with these options.

Z buffer shading mode. You can choose one of two modes for

shading TINpanels in 3Drendered viewing mode:

Flatshades each TINpanel a single colour. Flat-shaded objects

retain a polyhedral appearance.

Page 3163


21/128

Page 3163


Smoothassigns a colour to the centroid of each panel andblends the colours of adjacent panels at edges and vertices.Smooth-shaded objects appear curved.

Surface Attributes

In addition to path, names, and class, you can assign three attributes

which affect the display characteristics of an individual surface:

Panel colour. This parameter defines the colour in which the TINwill be drawn using the primary colour method.

Transparency. You can make surfaces transparent in order to see

data objects which are obscured from your line of sight.

Smoothing. You can always display smoothshaded panels in

rendered mode, regardless of program display settings.

If you choose the Triangle Dip option and you want to view a design

pit, you might define a colour profile called PIT-DIPwith these ranges:

0 to 1

1 to 15

15 to 60

60 to 90

RED

BLUE

GREEN

YELLOW

This range shows the tops of benches.This range shows ramps.This range shows bench slopes.

This range may show possible areas of slopefailure.

If you choose the Triangle Zoption and you want to view the same

design pit, you might define a colour profile called PIT-ELEVwith these

ranges:

1200 to 1240

1240 to 1280

1280 to 1320

1230 to 1360

1360 to 1400

RED

BLUE

GREEN

YELLOW

CYAN

First LevelSecond LevelThird LevelFourth LevelFifth Level

Page 3164


22/128

g


Surface Volume Reporting

You can instruct Gemcom to determine the volume below a surface to

a specified datum and issue a report. The resulting report includes:

Surface name.

Base elevation.

TotalXYarea (the sum of all triangle areas where each triangle is

projected onto theXYplane).

Total surface area (the sum of all triangle areas where each

triangle is projected onto its best fit plane).

Total volume between the surface and the base elevation.

Total triangles in TIN.

Average TINheight from base elevation. If the Zvalue of the

surface represents a grade value, this result gives the average

grade over the entire area of the surface.

Creating a SEG for Block Model InterfacingGemcom can create a SEGfrom a triangulated surface. When you

create a SEGfrom a surface, you can control the accuracy of the

process by specifying an integration level. A SEGcreated from polyline

data that preserves the feature breaks will give the truest possible

representation of the surface.

Page 3165


23/128

Modelling Chapter 9: Solids

Chapter 9

Solids

In This Chapter

Introduction

Using Solids Types of Solids

Solid Creation Guidelines

Components of a Solid

Component Requirements

Amalgamation of Sub-Rings

Dimples, Volcanoes, and Other Surfaces with Concavities

Recommendations Logical Solids

Solid Validation

Fixing Invalid Solids

Examples of Fixing Invalid Solids

Fixing Duplication Errors

Copying Solids

Intersecting Solids with Planes and Other Solids Contouring Solids

Displaying Solids

Introduction

Gemcom allows you to transform your 2D(two-dimensional) polygons

into 3D(three-dimensional) solids. A solid in Gemcom is a 3Dobject

that is created by first connecting polygons that define similar zones

from one plane to another using tie lines, and then by automaticallyconstructing a 3Dtriangulated surface around all the polygons and tie

lines. Gemcom can create solids that represent orebodies or

Page 3166


24/128


wastebodies, underground excavations and development such as

ramps or stopes, etc.

Using Solids

Gemcom provides you with a set of powerful interactive tools for

constructing 3Dsolids models (often called wire-frames). You can do

the following:

Create solids from combinations of polylines, points and 3Drings.

Create tie lines to link polylines, points and 3Drings to control

solid formation.

Intersect solids with surfaces and other solids.

Use solids to clip polylines.

Contour solids.

Create block models from solids.

Calculate ore reserves inside solids and block models.

Create new drillhole intersect data from solids.

For detailed procedures, refer to Chapter 13: The Solid Menu.

Types of Solids

The solids which Gemcom uses can be separated into three categories:

Geology solids. These are solids that represent homogenous

volumes of ground and have rock code and grade attributes.

Excavation solids. These are representations of voids left in the

ground by mining. These solids may represent planned miningexcavations or as-mined excavations.

Page 3167


25/128


Surfaces. .These are triangulated surfaces and are described in

more detail in Chapter 8: Surfaces.

Once created, a solid is a collection of triangular faces that encloses a

volume. Every triangle edge is connected fully to another triangle

edge. Consequently, there are no open areas or holes on the surface of

a solid. Each solid is given a series of names to uniquely identify the

solid, and a set of attributes that describes its properties.

Solids can be created as a single entity that is known as a physical

solid, having a single name and a single set of attributes to describe its

properties. Solids can also be created as a group of like entities that

are known as logical solids. Logical solids are also identified by a

single name and a single set of attributes that are applied to all of the

physical solids that form the logical solids. Once created, logical solids

are treated as a single entity (i.e., the same way as a physical solid).

An example of a physical solid could be a homogenous ore zone that is

one complete piece; an example of a logical solid could be a

homogenous ore zone that is broken into multiple zones, but is needed

to be treated as a single entity.

Geology Solids

Geological solids represent homogenous volumes of ground. Each

geological solid is identified by a three-part name, and is given a single

rock-type attribute, and single grade values for each specified mineral.

Geological solids are used to represent ore bodies, ore zones, dykes,

sills, or any other geological zone(see Figure 9-1). Geological solids are

generally constructed from combinations of 3Drings, polylines andpoints digitized on sections or plan views.

Page 3168


26/128


Figure 9-2: Examples of excavation solids

Figure 9-1: Examples of geology solids

Page 3169


27/128


Excavation Solids

Excavation solids represent voids in the ground created by mining.

Each excavation solid is identified by a three-part name, and no otherattributes. Excavation solids can represent development such as

shafts, haulages, crosscuts, ramps or raises, or stope designs.

Excavation solids can also represent excavation designs, or as-mined

excavations (see Figure 9-2).

Excavation solids can be constructed from digitized centrelines and

cross-section profiles, outlines digitized on plan views, 3Drings, orsurveyed data.

Note that solids are commonly viewed in combination with other solid

types and other data such as drillholes and block models for a more

comprehensive visualization of data. For example, Figure 9-3

illustrates geology and excavation solids, drillholes, and block models

together:

Figure 9-3: Combinations of data types viewed together

Page 3170


28/128


Solid Creation Guidelines

Solid models are created using three-dimensional triangulation that

links together sets of planar and non-planar collections of polylines.These collections of polylines can be combinations of open-ended status

lines, closed 3Drings and discrete points from drillhole intersects or

other sources. The triangulation and solid formation takes place after

you have linked the data elements together using three-dimensional

tie lines that may be complex polylines with multiple points. Careful

use and positioning of these tie lines allow you to apply extensive

control on how splits, bifurcations and end closures of solids arehandled.

Tie lines force specific points of one polyline to connect with specific

points on another adjacent polyline. At least one tie line connecting

two adjacent polylines is required in order for Gemcom to create a

mesh between them. All tie lines will be included as edges in the

triangular mesh that forms the solid. Tie lines therefore provide asmuch or as little control as you like over the shape of the final solid.

Figure 9-4: Two irregular polylines connected by four tie lines

Page 3171


29/128


It is recommended that you start by using a minimum of tie lines,

connecting pairs of polylines with one or two tie lines at logically

corresponding points. Gradually add more tie lines as required to

improve the shape of the solid or to resolve solid errors such as self-intersection. If polylines are highly irregular in shape, you may

achieve the best results by using extra tie lines in areas where it is

obvious that points match (see Figure 9-4).

Bifurcation (division into two forks) frequently occurs wherever one

polyline on a section must connect to two polylines on an adjacent

section. Adding a tie line split is necessary to divide the single polylineinto two sub-rings (see Figure 9-5).

Tie line split

Figure 9-5: Area of bifurcation

Gemcom will automatically create end closures (close-offs) at the ends

of a solid by determining which polylines are outermost (see Figure 9-

6). You may also need to create a close-off in an area of bifurcation,

using one or more tie line splits.

Page 3172


30/128


Because the creation of tie lines is typically the most time-consuming

part of solids modelling, it is highly recommended that you frequently

save the ties to disk.

Components of a Solid

The components you use to create a solid are as follows:

Rings

Ties

External points

Part-rings

Tie line splits

Polylines that "close-off" the

ends of the solid

Figure 9-6: Close-offs

Page 3173


31/128


Figure 9-7 illustrates these components together. The following

sections will discuss each component separately.

Figure 9-7: Components of a solid

tie line splits

tie lines

3D rings

part-rings

external points

Page 3174


32/128


Rings

A ring is defined as a 3Dclosed polyline (see Figure 9-8). The points

that form the polyline may or may not lie on a plane. In order to be

classified as a solid, an object must have at least one ring; otherwise,

the object is a surface.

Neighbouring rings can be at large angles to each other. Specifically,

for any sequence of three rings, the angle between the plane of the

first ring and the plane of the third ring must be less than 180.

Each ring must form a simple circuit when it is projected onto its best-

fit plane. As Figure 9-9 shows, a simple circuit means that the ring

does not intersect itself. If it does, the solid creation process will report

an error, and it will be necessary to modify the ring before attempting

the solid creation process again.

Figure 9-8: Rings

Page 3175


33/128


Sub-Rings

Rings can either be single entities, or they can be split into sub-rings

(see Figure 9-10) using tie line splits that connect points on the samering (as opposed to tie lines that connect rings on different planes).

Figure 9-10: Sub-Rings

OK ERROR ERROR

Figure 9-9: Rings must be simple circuits

A singlering withno splits

A ring splitinto sub-ringsby two tie lines

across its face

Page 3176

Ti


34/128


Ties

A tie is a polyline that connects other elements of the solid to each

other. A tie may have multiple segments. Each end of a tie lies on aring, a part-ring, an external point, or a split. Any number of tie lines

may start or end at the same point (see Figure 9-11).

Figure 9-11: Examples of ties

External Points

External points are used to terminate sections of the solid. These are

useful if you think there is part of the solid beyond the last ring, buthave no further hard data. You can place a point logically beyond the

last ring at an estimated location. You can think of an external point

as a one-point ring. An external point must be connected by at least

one tie (see Figure 9-12).

Page 3177


35/128


Part-Rings

A part-ring is a partial ring, i.e., it is not closed. A part-ring is usedwhen a full ring is not available. It modifies the solid surface in a local

area.

There are two types of part-rings:

Internal. An internal part-ring is internal in that it is logically

between other components of the solid (see Figure 9-13).

External. An external part-ring is external in that it is not

logically between other components. Instead, it is used to

terminate a portion of the solid, as per an external point (see

Figure 9-14).

Figure 9-12: An external point

Page 3178


36/128


Figure 9-14: An external part-ring

Figure 9-13: Internal part-rings

Page 3179


37/128


Tie Line Splits

Tie line splits are polylines that divide a ring into two or more sub-rings. Splits may have multiple segments. Each split starts and ends

on the same ring. Splits do not cross each other, nor do they join or

touch each other, except for possibly their end points. Splits are used

for bifurcation and/or close-offs. The area between the two highlighted

splits in Figure 9-15 forms a close-off that separates the legs of the

bifurcation.

Figure 9-15: Splits

Page 3180



38/128



The specific requirements for the components of a solid are very few.

However, it is important that the user understand them.

Requirements for Ties & Part-Rings

All part-rings need ties. External part-rings may be connected by ties

onlyto a logically adjacent full ring. A tie may not connect an external

part-ring to an internal part-ring, as shown in Figure 9-16. This isrestated here as a warning.

An external part-ring must not have part-rings for neighbours. In

other words, no part-rings are allowed between an external part-ring

and the adjacent full ring.

e1e2

e3

i1i2

i3

Figure 9-16: An incorrect data set

Figure 9-17 shows the correct use of an external part-ring.

!

Error: theinternal part-ring (i1, i2, i3)is not allowedbetween thefull ring andthe external

part-ring (e1,

Page 3181


39/128


a

bc

d

Figure 9-18: Ties to the ends of internal part-rings

Figure 9-17: A correct data set

The external part-ring isconnected directly to the full

Points a, b, c, and dare theends of internal part-rings.From each one there are twoties, in logically oppositedirections

Page 3182

Each end of an internal part-ring needs exactly two ties, one in each of


40/128


two logically opposite directions (see Figure 9-18).

Requirements for Sequences of Ties

Ties which join onto part-rings must be able to be joined into a

sequence of ties, at the points where the sequence crosses the part-

ring. The sequences must be completely separate, except possibly

where they join a full ring or external point. See the following

examples of correct and incorrect tie sequences.

The legend in Figure 9-19 applies to all example diagrams in Figure 9-

20 and Figure 9-21.

tie linesrings/part-rings

Figure 9-19: Diagram legend

Page 3183


41/128


A correct configuration

ap

Error: tieais not a member of a sequence of ties crossing part-ringp.

a b c

de

Error: sequencesabcandadego through, but they are not separate.

Figure 9-20: Example using two complete rings and two part-rings

Page 3184


42/128




Error: a sequence of ties does not cross the part-ring.

Figure 9-21: Example using two complete rings and one part-ring.

Page 3185

Requirements for Ties & External Part-Rings


43/128


The requirements for ties which join external part-rings are very

specific. The requirements are also very natural.

If an external part-ring has only one tie to it, the tie must be to one

end of the part-ring (see Figure 9-22).

OK ERROR

Figure 9-22: External part-ring with one tie

If an external part-ring has two or more ties to it, there must be one

tie to each end (see Figure 9-23).

OK ERROR ERROR

Figure 9-23: External part-ring with two or more ties

Requirements for Ties Between Two Full Rings

If two rings of the solid to be formed are connected by ties, there are

certain requirements for the ties.

For purposes of this section, we shall consider a sequence of ties to be

a tie, and will ignore ties which connect to splits. We will also ignore

part-rings.

In all cases, if your ties violate these rules, the program will highlight

the two rings and ask for more ties. You will need to add ties which do

not connect to a split. The best ties to add have end-points which arenot shared by other ties.

Page 3186

If the two rings are connected by a single tie, there are no further

requirements (see Figure 9-24)


44/128


requirements (see Figure 9-24).

OK

Figure 9-24: Two rings with one tie

If the two rings are connected by two ties, the four end-points of the

ties must all be different (see Figure 9-25).

OK ERROR

Figure 9-25: Two rings with two ties

If the two rings are connected by three ties, the three ties must have

at least five different end-points (see Figure 9-26).

OK: 6 end-pts

ERROR: 4 end-pts

OK: 5 end-pts

ERROR: 4 end-pts

Figure 9-26: Two rings with three ties

If the two rings are connected by four or more ties, there is no simple

concise rule. However, it is far better to have many different end-

points for the ties, than just a few shared end-points.

Page 3187

Requirements for Rings, Ties, and Part-Rings


45/128


Certain conditions exist which would result in ambiguities of data,

when dealing with rings, ties and part-rings:

Sprays of ties

Not enough ties

Ties which connect to splits

Sprays of Ties

Two rings or sub-rings connected only by a spray of ties is

ambiguous. A spray of ties is two or more ties with a single common

end-point (see Figure 9-27).

Figure 9-27: A spray of ties: you will be asked to supply more ties.

Page 3188


46/128


Not Enough Ties

When there is a pair of rings with exactly two ties, with one or more

part-rings, the case is ambiguous (see Figure 9-28).

Ties Which Connect to Splits

A tie may connect to any point of a split (see Figure 9-29).

Figure 9-29: A tie connecting to an interior point of a split

However, Figure 9-30 illustrates a requirement for additional ties. Thetwo ties need some assistance; by themselves it is not clear whether

Figure 9-28: Ambiguous case: you will be asked to specify more ties.

Page 3189


47/128


the ring on the far right forms a solid with either one of the sub-rings,

or both. The addition of ties which do not join the split is required to

resolve the situation.

Figure 9-30: Ambiguous case: you will asked to specify more ties.

Page 3190

Amalgamation of Sub-Rings


48/128


For purposes of explanation in this section, sequences of ties between

two rings will be considered to be a single tie. Also, part-rings will be

ignored.

Amalgamation of Sub-Rings on a Ring Face

Each ring has two faces, or sides, to it. When a ring is divided into sub-

rings, Gemcom makes a set of sub-rings for each face. The sub-ringsfor each face are then amalgamated according to these rules:

Firstly, ties which connect to a split are deactivated temporarily. The

reason for temporary deactivation is to ensure unambiguous

relationships between the sub-rings.

After temporarily deactivating ties which connect to splits, three rulescome into force for the amalgamation of sub-rings.

Rule 1:If sub-rings aand bare each tied to the same single sub-ring c,

then aand bwill be amalgamated into a single ring (on the side

connected to c) prior to forming the solid with c (see Figure 9-31 and

Figure 9-32).

Page 3191


49/128


Figure 9-32: Resultant solid

Figure 9-31: Illustration of Amalgamation Rule 1

These are the ringsand tie lines asthey exist beforesolid creation. Thetwo sub-rings onthe middle ring will

be amalgamatedwhen meshing tothe ring on the

The split in themiddle ring wasignored whenmeshing to theright ring, buthonoured whenmeshing to theleft one.

Page 3192


50/128



In Figure 9-33 and Figure 9-34, both the middle sub-rings are tied to

the rings on the right and left, so the middle sub-rings will be

amalgamated before forming the solid with the other rings. Note that

this action is different from methods formerly used in GEM-SOLID.


Page 3193


51/128



Rule 2:If sub-rings aand bare the adjoining sub-rings of ringR, and c

and dare the adjoining sub-rings of ring S, and ais tied to cand bis

tied to d, Gemcom will amalgamate awith band cwith dbefore

forming the solid (see Figure 9-35 and Figure 9-36).


Both sets ofsub-rings onthe face of eachring will beamalgamatedbefore formingthe solid.

Page 3194


52/128


Rule 3: If aand bare both tied to the same sub-ring c, but aand b

share no segments, this creates an error (see Figure 9-37).

Dimples, Volcanoes,

and Other Surfaces

with Concavities

Gemcom offers the capability to model surfaces with concavities. If a

solid has concavities on the sides, the concavities will be represented

in the rings, and solid formation will model the concavities without

further processing (see Figure 9-38).

Figure 9-38: A solid with a concavity on the side

Figure 9-37: An amalgamation error

Page 3195


53/128


If a solid has a concavity on the end, (e.g., if a close-off ring has a

dimple in it), you can model this readily, but in a different manner.

For example, a volcano would be modelled by constructing two solids:

1) a filled-in version of the volcano and 2) the plug at the top; and

then clipping the former against the latter using the solid operations

described elsewhere in this manual (see Figure 9-39).

Recommendations

The insertion of ties can have a very strong influence on the final

solid.

The filled-in volcano

The plug at the end of the volcano

The modelled volcano

Figure 9-39: Modelling a volcano

Page 3196

Controlling the Formation of Triangles

Let us look first at a simple example


54/128


Let us look first at a simple example.

n

f

A near ring nand a far ringf

n

f

With three ties added

One triangulation of the upper surface

Another triangulation of the upper surface

Page 3197

Figure 9-40: Alternate triangulations

Figure 9-40 illustrates that there are multiple ways of creating


55/128


triangles to form a solid. Note that different sets of triangles will give

different volumes, different cross-sections, etc.

If you have a preference for the triangulation of your solid, then it is

recommended that you place ties to express your preference.

Between ties, the program will choose triangles for you. You should

examine your solid carefully, and either add more ties or modify your

current ties to produce the solid that you want.

Ties with More Than Two Points

Your ties may have many points. This enables you to control the shape

of a solid in a local area.

However, if you use ties with more than two points, you may need to

control the triangles on either side of the multi-point tie. You would

exercise control of the triangles by placement of more ties (see Figure

9-41.)

Page 3198


56/128


Bidirectional Bifurcations

It is possible to create a solid which contains a bidirectional

bifurcation (see Figure 9-42).

A solid with a concavity

A possible triangulation.

A more conventional triangulation

Figure 9-41: Alternate triangulations

Triangles on theback side havebeen omitted for

Addition of thistie line restrictsthe influence ofthe concave tie.

Page 3199


57/128


Figure 9-42: A bidirectional bifurcation

The resulting solid will have two parts which meet only along a line.

This is not recommended practice. Triangles which adjoin the meeting

line will have more than the normal one neighbour per edge.

Zero-Thickness Portions of a Ring

It is possible for the data to produce solids in which some ringscontribute zerothickness portions to the solid. This is allowed as a

preliminary step to permit test-formation of solids, but is not

recommended for the final solid. Triangles on the two faces of the

zerothickness portions will have more than the normal one neighbour

per edge (see Figure 9-43).

Page 3200


58/128


Ties

Be generous when inserting ties, especially with ties that do not

connect to splits.

Logical Solids

A logical solid is simply a collection of physical solids which have

been designated as belonging logically together. A logical solid may be

useful in a zone in which the ore is extensively fractured, where each

physical solid represents a parcel of ore (see Figure 9-44).

Figure 9-44: Cross section through a logical solid

Logical solids are also used for nesting. Two solids are nested when

one fully encloses the other. For example, an orebody of one type could

contain an orebody of another type (see Figure 9-45).

a

Figure 9-43: A zerothickness portion of a solid

Page 3201


59/128


Figure 9-45: Cross section through a nested solid

The concept of nesting includes cases in which one solid fully encloses

multiple solids which may in turn enclose other solids, etc.

Volume Calculations for Logical Solids

Gemcom makes certain assumptions about each physical solid member

of a logical solid when performing volume calculations for the logical

solid.

Gemcom assumes that the physical solids which are outermost (i.e.,

not contained in any other physical solid) contribute positively to the

volume. The physical solids which are next to outermost contribute

negatively to the volume. The contributions of any other physical

solids continue to alternate according to their level of nesting.

Page 3202


60/128


In Figure 9-46, the volume of the logical solid is the volume of A minus

the volume of B plus the volume of C.

Solid Validation

Gemcom provides the capability for validating solids. It is strongly

recommended that you validate all solids upon creation (or upon

importation into Gemcom). Invalid solids can lead to incorrect

volumetrics as well as errors when intersecting solids with other solids

or surfaces. Early validation will help to ensure reliable results.

When validating solids, the program checks for invalid triangle edges

and self-intersection. To be valid, a solid may not intersect itself. A

solid is self-intersecting when one part of the solid intersects another

part of the same solid (i.e., when any of its triangles intersect each

other). As well, each edge in a valid solid must be part of only two

A

B

C

Figure 9-46: Cut-away drawing of a nested logical solid

Page 3203

triangles (or one triangle in the case of edges along the perimeter of a

valid surface).

Whenever a solid is validated, the program looks for self-intersecting


61/128


, p g g

triangles and counts triangle edges to determine if any are connectedto more edges than allowed. If any errors are discovered, Gemcom

displays an error message and highlights the problem areas.

Fixing Invalid Solids

There are a number of situations that give rise to problems associated

with solid construction. Most of the problems are related to the

varying shapes or odd placement of the polygons (3Drings) being

meshed.

The first step in fixing an invalid solid is to inspect the area(s)

identified by the program as containing self-intersecting triangles orinvalid edges. Gemcom allows you to form a solid (or save polylines) of

the incorrect triangles to facilitate the inspection. If the original solid

was formed from ties and rings, you can display the bad triangles

with the original ties and rings.

There are several strategies for correcting invalid solids:

Strategic placement of tie lines.Oneway to eliminate self-

intersection is to change or add tie lines. The original placement of

a tie line may be forcing the creation of triangle edges in an

inappropriate direction.

Adding full or part-rings. Full or part-rings can be added

between rings to maintain separation.

Changing or adding tie line splits. Since all tie lines (including

splits) can have multiple points, you can add points to change the

shape of the split. Alternatively, you can put in two splits close

together, which creates a small close-off between them. This will

separate the two legs of a bifurcation a small amount. Or, you can

create tie lines from a split to a ring to improve the triangulation.

Page 3204

Adding nodes or thickening the 3Drings. You can resolve

solid self-intersection by thickening the rings or the ties (or both).

Thickening is the process of increasing the density of points along

a line. However, the thickening of lines may produce more


62/128


a line. However, the thickening of lines may produce more

triangles in the solid than actually required, thus unnecessarilyincreasing the processing time and the memory needed. For these

reasons, this strategy should be used sparingly: it is usually best

to add nodes manually in only the problem areas.

Another possibility for correcting invalid solids may be the

modification of the original 3Drings. While this can solve meshing

problems, it is usually undesirable given that the purpose of solidbuilding is to create a solid that conforms to defined 3Dshapes.

Examples of Fixing Invalid Solids

Three examples are presented here of common situations that canproduce invalid solids or surfaces. For each example, we will outline

the steps that can be taken to correct (or prevent) the problems. For

simplicity of illustration, we will use solids being created with two or

three 3Drings at a time.

The example dataset is a series of 3Drings that represent the

lithological extent of a vein structure (see Figure 9-47). Each ring hasbeen digitized on section. However, they are non-planar, meaning that

some points have been digitized at distances in and out of each section.

The first example illustrates the steps used to correct an invalid solid

that was created from two 3Drings that are varying in both shape and

size. The other examples illustrate cases where the narrowness of

rings and their positions relative to each other are the critical factorscausing problems.

Page 3205

10500E

10400E

10350E

10150E


63/128


Changing Tie Lines

In the first example, we will create a solid by meshing the 3Drings on

section 10500E and 10550E. In the first attempt, we place one tie line

connecting the top of each ring (see Figure 9-48).

10550E10200E

10150E

West

Figure 9-47: 3Drings on sections from the example dataset

Page 3206

Section10500ETie line


64/128


Figure 9-49 shows the resulting solid. However, upon validating the

solid using Solid }}Options }}Check Solid/Surface Validity, we find

Section10550E

Figure 9-48; Original placement of tie line

Figure 9-49: Resulting solid

Page 3207


65/128


that the solid has twenty-four self-intersecting triangles (see Figure 9-

50).

We save the bad triangles as a solid so that we can display the exact

location of the problem areas onscreen (see Figure 9-51). All other

solids are turned off or de-selected.

We can now see that there are two self-intersecting areas. We shall

examine each one.

Figure 9-50: Solid verification status box

Area B

Area A

Figure 9-51: Bad triangles displayed as a solid

Page 3208

Ring 10500E


66/128


Two conditions are causing the self-intersection of triangles in Area A.

The first is related both to the placement of the original tie line

connecting the 3Drings and to the varying shape of each ring.

The solid creation process normally connects nodes on one ring that

are proximal to nodes on a connected ring. The placement of a tie lineoverrides this normal construction process and alters which nodes will

be connected to others. In Figure 9-52, the triangular edges that make

up Area A are oriented in the same direction as the tie line. This is

causing unnecessarily long triangular edges, resulting in self-

intersection.

The second condition in Area A is the shape of the 3Dring on section10550E (the shorter ring). The narrowness of this ring increases the

probability of self-intersecting triangles, especially when the

triangular edges are long.

The problem in Area B is quite evident in Figure 9-52: the triangular

edges are intersecting the back face of the solid on ring 10500E. As in

Area A, the self-intersecting triangles are a result of two conditions.Again, triangle edges are unnecessarily elongated because of a solid

Area A

Area B

Narrow

3D ring

Tie line

Ring 10550E

Figure 9-52: Close-up of problem areas

Page 3209

creation pattern that is based on the poor placement of the tie line.

The second condition is due to the meshing of non-planar rings

(creating the bend at Area B).


67/128


Both areas can be easily corrected. The key is to determine a commoncondition contributing to both problems. Since unnecessarily long

edges occurs in both areas, it follows that we should direct our

attention to changing the placement of the original tie line. A better

placement is illustrated in Figure 9-53:

New tie lines

Figure 9-53: New placement of tie line

Placing two tie linesin this manner should

reduce the chance ofunnecessarily longtriangle edges.

Page 3210


68/128


Notice the new orientation of the resulting triangle edges in Figure 9-

54, when compared to the original solid. Another validity test finds

that none of the triangles self-intersect. The new solid is valid.

Adding Nodes and Part-Rings

Our second example examines the same problem of self-intersecting

triangles between 3Drings. In this case, the bottom of the solid is

visibly intersecting the top of the solid. We are using sections 10350E

and 10400E:

Figure 9-54: Resulting solid

Page 3211

Section

10350E

Section

10400E


69/128


Area C

Area D

Figure 9-55: Bad triangles displayed as solid

As seen in Figure 9-55, we have placed the tie lines so as to eliminatethe possibility of self-intersecting triangles in Area C. However, after

validating the solid, we see that triangles self-intersect in Area D.

When the area of self-intersection is rendered, the bottom of the solid

can be seen peeking through the top. In the 3Dview (Figure 9-56), we

can see that the narrowness of the 3Drings is a factor, combined with

the unnecessarily long triangular edges. In the 2Dview (Figure 9-57),we can also observe that the sharp and narrow bend on ring 10350E is

contributing to the self-intersection.

Page 3212


70/128


Two strategies for correcting the solid are possible.

Bottom of solid

protruding

through the top

Figure 9-56: Rendered 3Dview of problem area

Ring on section

10400E

(foreground)

Area of self-intersecting

triangles

Tie lines

Ring on section

10350E

(background)

Sharp andnarrow bend

Figure 9-57: 2Dview of section, looking west

Page 3213

Additional


71/128


The first is to insert part-rings between both rings. These part-rings

force the solid creation process to maintain some solid thickness

between the original rings, thus reducing the chance of self-

intersection.

The second strategy would be to insert more points along both rings inthe area of self-intersection. Adding nodes reduces the length of

triangular edges, thereby minimizing the chance of self-intersection.

Nodes are added using Polyline }}Multiline }}Thicken.

In Figure 9-58, we add two internal part-rings in the area of the

problem. An extra node is also inserted on ring 10400E to provide an

anchor for the back face of the part-ring. The resulting solid is correctwith no self-intersecting triangles.

Figure 9-59 shows another way we could have corrected the solid. The

addition of nodes and a few extra tie lines for control appears to be the

easiest strategy.

Additional

node

Two part-rings

Additional

tie lines

Additionaltie lines

Figure 9-58: Adding two part-rings

Page 3214

Ring has been

thickened


72/128


Adding 3D Rings

Gemcom performs validity checks on a hierarchical basis. The process

first looks for invalid edges, and then for self-intersecting triangles. Ifthe system encounters invalid edges, it will discontinue any further

checks for self-intersection.

Invalid edges occur when three or more triangles share an edge. The

most likely occurrence of this is in areas of bifurcation, when the

inside surface of the solid becomes coincident with itself: part of the

surface may internally touch another part of the surface. You can

visualize this by thinking of squeezing a balloon: where your thumb

and index finger touch each other would be an invalid edge.

In the following example, our attempt to validate a solid created from

rings on sections 10150E and 10200E produces the error message seen

in Figure 9-60:

Ring has been

thickened

Figure 9-59: Adding extra nodes and ties

Page 3215


73/128


The error message indicates that the meshing process has detected

one bad edge. The problem area is located along the edge of

bifurcation (see Figure 9-61).

Section

10150E

Section

10200E

Tie line (line of

bifurcation)

Tie line

Tie line

Figure 9-61: Placement of tie lines for bifurcated solid creation

Figure 9-62 shows that the four bad triangles have a coincident

edgethe line of bifurcation.

Fortunately, the solution is simple. By adding another ring adjacent to

section 10150E, we can force the back side of the solid away from the

Figure 9-60: Solid verification status box

Page 3216

Badtriangles


74/128


plane containing the line of bifurcation. Since the ultimate goal is to

create a solid for all rings, we can add the needed ring by simply

activating the ring on the next section (10100E). We then add some tie

lines and create a solid using all three sections (see Figure 9-63).

If no other sections had existed in our dataset, we could have copied

the ring on section 10150E and placed the duplicate a small distancewest of the bifurcation. We would then construct the solid by

Bad triangles

Bad edge(coincident with tie linedefining line of bifurcation)

Figure 9-62: Rendered 3D view of the four bad triangles

Ring on section10100E

Area of

bifurcation

Figure 9-63: Adding a new 3Dring

Page 3217

connecting the duplicate ring with the ring on section 10150E with as

many tie lines as necessary.

Remember that after you fix invalid edges, you must validate the new

solid to check for any self-intersecting triangles that were previouslyignored by the validation process


75/128


y g g p yignored by the validation process.

Fixing Duplication Errors

Figure 9-64 shows a common error message encountered during solidcreation:

Figure 9-64: Solid creation error message

However, your dataset of 3Drings may clearly show that all tie line

endpoints are connected to only one ring. The problem is often that

some of the rings are duplicated and thus not readily visible. You may

have unintentionally produced this situation by loading a dataset of 3D

rings or tie lines more than once.

You can check for duplicate rings, lines, or tie lines by activating all

lines and running the consolidation process using Polyline

}}Multiline }}Consolidate. This process checks for duplicate lines and

segments and eliminates them in one step.

Copying Solids

You can create a new solid by copying and renaming an existing solid.

The new solid will contain the same attribute information as the

Page 3218

original. This option can be used to make a temporary backup copy of

any solid prior to performing editing operations.

As this option allows you to enter X, Y, and/or Z offset values, you can

copy and move a solid in one step. For example, if for some reason asolid is in the wrong location but you know the XYZ offsets that would


76/128


py p p ,solid is in the wrong location but you know the XYZ offsets that would

correct the error, by giving the new solid the same name as the

original you can overwrite the original solid in the proper position.

Intersecting Solids with Planes and Other SolidsYou can create solids by intersecting solids with other solids, surfaces

or planes. You can calculate and view these intersections at any

orientation in both 2Dand 3D. The ability to intersect and combine

solids is an extremely powerful feature of the solids modelling

capabilities of Gemcom.

Figure 9-65: Two intersecting solids

Examples operations refer to the sample solids in Figure 9-65. You can

interactively select solids with the mouse and then do the following:

Create the polyline of intersection between two solids.

Clip a solid inside or outside a polygon.

Clip the portion of a solid that lies above or below a surface.

Clip the solid portion of a solid that lies inside another solid (see

Figure 9-66).

Page 3219


77/128


Figure 9-66: Solid A clipped by solid B

Intersect solid with another solid (see Figure 9-67).

Figure 9-67: Solid A intersected with solid B

Create the union of one solid with another solid (see Figure 9-68).

Figure 9-68: Union of solid A and solid B

You can use the solid-to-surface intersection options to assist in

building accurate geological models, for example, by trimming

Page 3220

geological solids with surfaces that represent fault planes, or by

trimming solids that protrude above surface topographies.

The solid-to-solid options can be effectively used to add further control

to the shapes of solids representing ore zones, or can be used invarious underground mine planning functions when solids are being


78/128


g p g g

used to represent mine development, stopes or other excavations that

require trimming or combining.

Intersecting Logical Solids

As with any solid, a logical solid should not intersect itself; surfaces of

the member physical solids may not intersect each other. Therefore, it

is strongly recommended that you avoid cases in which the physical

solids touch or intersect at a point or a line, or nearly at a point or line

(see Figure 9-69 and Figure 9-70).

Figure 9-69: Two solids intersecting in a single point

Figure 9-70: Two solids intersecting in a line segment

Page 3221

If any of these conditions exist, you should change the solids slightly,

by placing a significant amount of space between them (e.g., 0.1

metre).

Intersection operations between logical solids produce the same

intuitive results as for physical solids. However, intersections between


79/128


a surface and a logical solid make sense only when the surface

intersects all of the physical solids members of the logical solid. If the

surface misses any of the physical solids, the result will be undefined.

Fixing Invalid Solids After Intersection

The intersection of solids requires complex computations for many of

the triangles which make up the solids. In isolated instances, the

newly created solid may have triangles with extreme properties which

render it invalid. However, temporarily shifting one of the solids a

small amount (e.g., two millimetres in elevation) will usually resolve

the problem.

Contouring

Contouring involves slicing solids with sets of parallel planes (see

Figure 9-71 and Figure 9-72). Contour lines are the polylines ofintersection between the solid being contoured and the parallel planes.

The contour lines are stored as polylines, so once they are created they

can be edited, smoothed, manipulated or used in the same manner as

any other polyline. This means that you can create solids from sets of

polylines on vertical sections, create contours on plan views, edit the

polylines that were created in the contouring process, and then rebuild

the solids from the plan view data to get a new interpretation of your

data. You can define the planes in a number of ways:

As horizontal planes, by specifying the upper and lower elevations

and the separation distances between the planes.

In the current view plane, with an upper and lower local Z value,

and separation distances between the planes.

Page 3222


80/128


As the current view plane.

Using all active vertical sections.

Using all active plan views.

Using all active inclined sections.

The resulting solid/surface/plane intersections will be saved as

polylines. The attributes assigned to these polylines will depend on

both the user inputs and the attributes and class of the contoured TIN.

Figure 9-71: Contours from a solid using vertical sections

Figure 9-72: Contours from a solid using plan views

Page 3223

If you are contouring Geology class solids, the resulting polylines

will be stored as 3DRing polylines and will inherit the rock code

from the solid.

If you are contouring Excavation or Surface class TINs, the

polylines will be stored as Status Line type and will be assigned

h d f l l


81/128


the default status line type.

If you are contouring pre-defined planes (for example, all vertical

sections), the plane attribute of the polylines will be assigned

based on the section name.

You can preset default values for all the polyline attributes if you dontwant the program to automatically assign the attributes for you. The

polylines created from contouring can be used for all normal polyline

operations (clipping, solid creation, editing, etc.).

Displaying Solids

Each TINcreated within Gemcom (or imported into Gemcom) belongs

to one of three classes: Geology, Excavation or Surface. All active TINs

are displayed based on their class assignment. You can define different

display parameters foreach classat any time. These parameters

include:

Solid display mode. You can choose one of two modes for

displaying the TIN.

Solid fillshows the TINwith solid coloured panels (whenviewed in rendered mode).

Wireframeshows only the TINedges and no panels.

Obtain colour from. Gemcom can use one of three methods to

assign a colour to each individual triangle within the TIN:

Primary colourmethod colours all triangles the same,according to the colour assigned to the TINwhen it is created.

Triangle dipmethod colours each triangle based on its dipangle (in degrees). This option is very useful in cases where the

Page 3224

triangle dip values are critical, for example, in pit design orslope stability work. Gemcom can provide a very fast graphicaloverview of the slopes of your entire TIN.

Triangle Zmethod colours each triangle based on the Z value

of the triangle centroid.


82/128


Colour profile for display. The Triangle Dip and Triangle Z

display options require a colour profile to be defined that provides

colours for all possible value ranges. It is generally a good idea to

define colour profiles specifically for viewing TINs with these

options.

Z buffer shading mode. You can choose one of two modes for

shading TINpanels in 3Drendered viewing mode:

Flatshades each TINpanel a single colour. Flat-shaded objectsretain a polyhedral appearance (see Figure 9-73).

Smoothassigns a colour to the centroid of each panel and

blends the colours of adjacent panels at edges and vertices.Smooth-shaded objects appear curved (see Figure 9-74).

Figure 9-73: The flat-shaded sphere displays a polyhedral, "golf ball"

appearance

Page 3225


83/128


Solid Attributes

In addition to path, names, and class (and grades for Geology solids)

you can assign three attributes which directly affect the display

characteristics of an individual solid or surface:

Panel colour(for excavations or surfaces) or Geological code(for geology solids). This parameter defines the colour in which the

TINwill be drawn using the primary colour method, either

explicitly or via the rock code profile.

Transparency. You can make solids and surfaces transparent in

order to see data objects which are obscured from your line of

sight. When you define multiple overlapping transparent solids,Gemcom may make some of them opaque for clarity.

Smoothing. You can always display smoothshaded panels in

rendered mode, regardless

Documents

Surfaces Gemcom