Computer-Generated Computer-Generated Pen-and-Ink Illustration of TreesPen-and-Ink Illustration of Trees

Oliver Deussen &

Thomas Strothotte

University of Magdeburg

The Idea

• Standard NPR papers have not specifically focused on foliage

• Current NPR plant models are generic…

• …Even though we can create specific species models

• Let’s start with an exact model and remove unnecessary geometry

Giving Away the Ending

Tree model generated with the xfrog system Pen-and-Ink illustration of the complex model

Standard Issues in Traditional Tree Illustration (1)

• The tree skeleton (trunk) is usually drawn up to the 2nd branching level– Prominent silhouette lines– Crosshatching for shading

• How do you determine silhouette?

• Where do you place the crosshatches?

• How high is high enough?

Standard Issues in Traditional Tree Illustration (2)

• Foliage is composed of 3 areas:– Top is usually well-lit, so minimal detail shown– Half-shadow areas show more foliage detail– Deep shadow regions (many techniques used)

• What shape are the leaves?• What shading techniques to use (black,

increasing leaf silhouette detail, thicker lines)?

And So, To Begin...

• 2 Files for stored model– One for the trunk (to 2nd branching level)– One for the leaves (pos. & normal)

• Trunk is drawn using traditional NPR algorithms

• Leaves are drawn with some primitive and assigned detail based on depth-difference algorithm

The Tree Skeleton

• Uses Markosian’s or Rakar & Cohen’s silhouette algorithms

• Crosshatches placed with the Difference Image algorithm or a Floyd Steinberg variant

The Fun Part: Leaves (!)

• System uses Zero-Order derivatives for determining important lines on a surface

• Outlines are drawn if the maximal depth difference of the leaf to neighboring leaves is above a certain threshold– Draw the leaves as solids & get depth buffer– For each pixel, find out how far it is in front of its

neighbors– Use that data to draw the leaves

Big Ol’ Equation Time

• d0 & d1 = min and max values represented in the depth buffer

• z0 & z1 = corresponding depth values of near & far clipping planes in camera projection

• d = depth value [0..1]• z = depth in camera coordinate system

More Equation Stuff

• Depth differences can be computed for eye coords or directly for depth buffer– Latter method results in larger changes

• Depth difference threshold is determined by a percentage of the depth range of the tree

• Other numbers:– d0 = 0 & d1 = 65535

– z0 = 1 & z1 = 11 (approx. for real trees)

Varying Equation Inputs

- Disc size = 0.15- Threshold = 1000

Tree 1 with varying primitive size & threshold

- Disc size = 0.7- Threshold = 2000

• Essentially, here’s what you get:– Since depth buffer differences are non-linear,

you get detail up front & less in the back

– Changing ratio of z1 to z0 alters non-linearity

– Primitive size based on the depth of the tree

Free LOD

Primitive size & threshold constant Primitives enlarged with distance

Primitive Choices

• Primitive shapes can also be altered for a more accurate representation of real leaves– one could use an actual 3D model...

– …or use a subset of possible views

Shadow in black, threshold = 1000 Shadow by detail, threshold = 6000

The Software Framework

• 1: Determine depth differences– Interactive: both stem & foliage done together

• 2: Software shadows are created & stored

• 3: Draw the pixels above the threshold

• For higher-quality images:– Vectorize the stem & foliage bitmaps separately

• least-square fitting

• index buffer (stores primitive ID)

– Draw polygons by spline interpolation

Results & Measures• (a): 13,200 elliptic

primitives - 10 seconds (SGI Octane (Maximum Impact))

• (c): 200,000 leaves reduce to 16,200 particles

• (f): 90,000 tree particles, 23,000 grass particles - 1 minute

• Interactive: 3 trees of 20,000 particles each and 25,000 ground particles at 3 frames/sec (SGI Onyx 2)

Conclusion & Questions

• Future Work:– Crosshatching on the leaves– Needs continuous LOD– Cartoons & other non-realistic effects

• My Questions:– What, exactly, is d?– Advantages over previous (non-species-specific)

efforts?– 3 frames-per-second. Gee, that’s helpful.