CS348b2007

Project Writeup : Sakura ("Cherry Blossom")

Team

Inspiration Images

Overview

Tree Overview

Procedural Tree Generation - Tom

L-system Background

Probability Distribution Function Implementation

* Bottom radius * Top radius * Height * 3D Rotation and Translation * Gnarling

Tree Rendering (Tom)

http://www.nbb.cornell.edu/neurobio/land/OldStudentProjects/cs490-94to95/hwchen/pp1.gif

Tree Design Evolution

Basic Texture, No Branching

Basic Branching, Lighting

Model Leaves, Perspective

True Branching, Cherry Tree Properties

Gnarled Rotations, Proportional Trunk

Smooth Gnarled, Reduce Leaf Noise

Increase Triangle Count, Decrease Sudden Knobs

Natural Bark Perturbation With Displacement Mapping

First Render (no lighting, didn't pick a good tree model)

Second Render (slightly better lighting, backup, better model)

Third Render (backdrop, lighting)

Fourth Render (striped texture)

Fifth Render (correctly colored texture)

Sixth Render (enlarged, texture and bump mapping)

Seventh Render (fixed jaggy artifacts, basic lentical bark)

Eighth Render (displacement mapping for more realism)

Ninth Render (backdrop)

Ninth Render (different model)

SpeedTree Implementation (for reference)

Procedural Bark (Tom)

Texture Generation

0307-sakurabark-1200

Texture Mapping (Tom)

Classic Plane Curves

Background

Prunus serrulata are dicots and possess five petals, five sepals, several stamen and a pistil.

We observed that in this case that the beauty of nature coincides with the beauty of mathematics. More specifically, the shape and geometry of these blossoms can be recreated with curves defined in polar coordinates.

Blossom Rendering (Priscilla)

We chose curves that most closely resemble the shapes of most importantly the petals and sepals. The following is a diagram of the parts of a typical dicot:

The shapes of the petals resemble cardioids:

... and the placement of the petals are similar to the maxima of the 5 petal rose curve:

The star shape and positioning of the sepals resemble a 5 point hypercycloid:

This is a mathematica modeling of a single petal, with the commands used:

All petals together:

and then with varied sine and cosine noise added to the z-component as well as variance in curvature, so that the petals are not completely flat and emulate the imperfection in nature:

The petals are cardioids with the z-coordinate following the shape of a paraboloid to create the upcurving effect of the petals. The position of the petals around the center of the blossom are calculated according to those of the 5 petal rose curve.

The following is a Mathematica model of the sepals plus the stem:

The pistil and stamen are relatively straightforward to generate, as they are just segments with ellipsoids at the end.

The following is a plain PBRT rendering of the final bare model:

Here is one of the images where I experimented with color, texture, and environment map infinite lighting. Notice also a rotated version where the sepals are displayed prominently:

Here is some experimentation with "dramatic" spot lights. lt gave a poor effect, as spot lights usually give a harsh appearance:

Texture Mapping (Priscilla)

After petal generation has concluded, we planned to generate randomized veins on the petal (all originating from the center) with a jitter transform and/or Worley cellular texturing (procedural). The vein pattern for the petals is actinodromous venation, in which three or more primary veins diverge radially from a single point. Primary veins support sequences of secondary (lateral) veins, which may branch further into higher-order veins. The secondary veins and their descendants may be free-ending, which produces an open, tree-like venation pattern, or they may connect (anastomose), forming loops characteristic of a closed pattern. Tertiary and higher-order veins usually link the secondaries, forming a ladder-like (percurrent) or netlike (reticulate) patterngrid size in every simulation step, which precludes continuous simulation of growth. Vein segments are straight, and segments double in length in each growth step, which yields artificial-looking long straight lines running through the pattern. [7] Due to time constraints, however, we were not able to devote time to this idea.

Subsurface Scattering (Priscilla)

Subsurface scattering (or SSS) is a mechanism of light transport in which light penetrates the surface of a translucent object, is scattered by interacting with the material, and exits the surface at a different point. The light will generally penetrate the surface and be reflected a number of times at irregular angles inside the material, before passing back out of the material at an angle other than the angle it would reflect at had it reflected directly off the surface. (Wikipedia)

Background

Rose petals are translucent and to achieve the realistic, silky, lifelike softness we must implement SSS. This may be achieved with the reflection model described in the paper by Hanrahan/Krueger. We will also study the structure and cellular layers of petals. So far, we have learned that two especially characteristic layers, such as upper epidermal cells which are dome-shaped and spongy cells which reflect much light, cause the unique appearance of rose petals.

[9]

Petal SSS

I wrote a new petal material plugin to PBRT, which added the BxDF per Hanrahan and Krueger. I noted that in the diagram above of the cellular layers of petals was significantly less and thinner than the leaf diagram that the paper mentioned and took this as a justification of using the first order approximation for backscatter and the zeroth order approximation for the transmittance. I will calcuate the radiance by summing the radiance from surface and subsurface scattering, and the transmitted radiance from the sum of the radiance from absorption and subsurface scattering. From these values I calculate the BRDF and the BTDF and take into account the Fresnel coefficients. I used an index of refraction of 1.37 which is reasonable for epidermis of skin.

For setting the specular and diffuse values I used a color picker in The Gimp on the model image.

Final Single Sakura Blossom

One Blossom Next to Tree

Final Image

Links

last edited 2007-06-13 17:47:47 by PriscillaPham