Drawing in the Digital Age by Wei Xu, Ph.D.Chapter 2 Part 1

Extracting Graphical StructureA Scientific Point of View

Presentation by Honoria Starbuck, Ph.D.

Computer graphics (CG) scientists develop techniques for movies and video games.

• These techniques are designed to make processing and storing graphic data accurate and fast.

• Some of these CG principles are applicable to traditional drawing.

• Let’s take advantage of existing approaches…

– How objects are structured– Spatial properties of shapes– What graphical structures should be extracted for drawing

purposes– How triangulation is used to extract graphic information

Multiresolution or hierarchical approach.

• In Computer Graphics (CG), resolution means the degree of detail or complexity.

• In drawing, a multiresolution approach means to draw big shapes first and details last.

Progressive/adaptive refinement and big shapes first!

Progressive/adaptive refinement is a strategy associated with multiresolutionapproaches.

Typically, we express a target problem in a hierarchical structure so that we can access the lowest level first and gradually add details to achieve higher quality.

Boolean operations are WHAT????

Boolean operations represent mathematical logic processes that integrate two sets or objects.

By using these operations—called union, intersection, and difference—a variety of results can be generated from two given objects.

Booleans, the Thinker, and You

Boolean operations offer a powerful mechanism to deconstruct a complicated object into simpler and smaller parts.

Obviously, we can apply these operations repeatedly on the subobjects to divide everything further into trivial items. This treatment is a direct application of the divide-and-conquer strategy in dealing with geometric objects.

Primary Forms

Primary Forms In a 3D physical space may have various appearances.

Some are smooth, some are rough, some are complicated, and some are simple. In order to study their behaviors, mathematicians have simplified and categorized objects into several primary forms: spheres, cubes, cylinders, cones, and torus

Make a tree!

A constructive solid geometry (CSG) tree is a graphic representation that is used by computer-aided design (CAD) software to build 3D objects with the primary forms.

A CSG tree is a mathematical tool used to analyze the internal structure of an object. More important, its process is designed so that it can be used directly to assemble objects with Boolean operations step-by-step.

Combine primary forms to see to draw.

1. Analyze the internal structure of an object2. Assemble primary forms to build the object’s structure,

placement, and proportions

Make a bounding box!

A bounding box is the tightest box that can surround an object, no matter how complicated that object is.

Thus, a bounding box is a simplified version of the original object.

The major purpose of a bounding box is to describe the size, proportion, and location of an object without processing its detailed information.

Make a bounding polygon!

Bounding polygons can approximate the silhouette of an object very closely.

Therefore, polygons are helpful in drawing.

Concave and Convex Polygons

Which group of polygons is concave?In math, a polygon is convex if none of its internal angles is more than 180°; otherwise, it is known as concave.

A concave polygon looks sort of like a vertex has been 'pushed in' towards the inside of the polygon.

Quiz

1. Make a bounding polygon for Spongebob2. Make a bounding polygon for BB83. Make a bounding polygon for R2D24. Make a bounding polygon for your pet.5. Make a bounding polygon for a student seated

across the room from you.6. Draw a concave polygon.7. Draw a convex polygon.

What fun!

Triangulation

https://youtu.be/cdEHtxeO4aE

Triangulation is an important technique used in CG for managing spatial information. For a given set of points in an image, we can connect them to form a triangle mesh that covers the entire image. The main purpose of triangulation is to partition a 2D region into triangles so that all structures under the triangle mesh can be quickly located and studied.

Extra Credit: Low Poly Self Portrait

Triangulate yourself

https://youtu.be/h7XTn72N1zk

Images on the Picture Plane

To find a universal method suitable for drawing any scene, we must first answer this fundamental question:

What is the common and essential element of all scenes?

A simple answer is –

the images on the picture plane.

What’s the picture plane again?

• in perspective, the imaginary plane corresponding to the surface of a picture, perpendicular to the viewer's line of sight.

Role of basic shapes in drawing.

These basic shapes serve as the building blocks of observational drawing.

For beginners, it is essential to learn how to handle these simple shapes efficiently on paper. This is akin to the “addition” operation when learning math. You have to master it before moving to an upper level.

The good news is that most people don’t have any trouble copying these shapes. After an entry-level artist has acquired the skill to draw basic shapes, drawing theories and techniques will help that artist conquer all types of complicated shapes and combinations.

Simple shapes: Big Money

http://video.disney.nl/videos/star-wars-the-force-awakens-designing-bb8-52faa8de848ac6e989d3d09e

J.J. Abrams rough sketch for BB8

Play: Make something using basic shapes.

Vocabulary

• Picture Plane• Basic Shapes• Polygon• Bounding polygon• Concave• Convex• Computer Graphics (CG)• Multiresolution in drawing• Hierarchy

Works Cited• Abrams, J.J. Rough Sketch for BB8 Droid. http://i0.wp.com/bitcast-a-sm.bitgravity.com/slashfilm/wp/wp-

content/images/ZZ725DA238.jpg

• Concave Polygon. MegaMindAcacdemy. http://megamindacademy.com/concave-polygon/

• Disney. The Force Awakens: Designing BB8 http://video.disney.nl/videos/star-wars-the-force-awakens-designing-bb8-52faa8de848ac6e989d3d09e

• Geometry Polygons. Convex and Concave Polygons. Sparklenotes. http://www.sparknotes.com/math/geometry1/polygons/section2.rhtml

• Helquist, B. 2013. How to Draw a Grumpy Goat.• http://bretthelquist.blogspot.com/2013_04_01_archive.html

• Lundgren, M. Drawing Simple Shapes. http://lundgrenart.weebly.com/drawing-simple-shapes.html

• Picture plane. 2014. Animation Tutorials.http://www.animationbrain.com/three-point-perspective.html

• Southpark art. 2015. http://insidepulse.com/2015/10/16/10-thoughts-on-south-park-youre-not-yelping/