The following 942 words could not be found in the dictionary of 615 words (including 615 LocalSpellingWords) and are highlighted below:

13th   20th   22nd   2mod   2sakura   520ed3efcd   abort   above   absorption   According   according   achieve   achieved   acm   actinodromous   adaptation   add   added   adding   addition   affect   against   air   algorithm   all   All   allow   allowed   along   although   am   among   an   An   anastomose   and   angle   angles   animation   Annual   annual   another   appearance   Application   application   applied   apply   approach   approximation   ar   arbitrary   ared   arnumber   around   artificial   associated   at   attachment   attempted   August   Author   axiom   axis   back   backdrop   Background   Backscatter   backscatter   bare   bark   Bark   base   Based   based   Basic   Battjes   be   beautiful   beauty   became   become   been   before   begin   begins   Below   below   better   between   biology   Bloss   Blossom   blossom   blossoms   Bottom   bounds   Branch   branch   branches   Branches   branching   Branching   bump   Bump   bumpiness   but   Bx   by   calculate   calculated   calculating   called   camera   can   capture   Cardioid   cardioids   case   cause   cells   cellular   center   certain   cfm   challenge   characteristic   Cherry   cherry   Chicago   chose   chosen   circular   citation   citeseer   Classic   closed   closely   coefficients   coincides   coll   Collision   color   commands   competition   completely   component   composed   comprehensive   computed   computer   Computer   concluded   Conference   conference   connect   consists   constraints   constructed   continue   continuous   contours   control   controls   coordinate   coordinates   cosine   Count   created   creating   Creation   Crink   crinkcode   crinkles   cross   Cross   cs348b   curvature   curve   Curves   curves   curving   cutoff   Cylinder   cylinder   cylinders   Deborah   Decrease   decreased   defined   defines   demonstrate   depending   depth   descendants   described   design   desired   details   diagram   dicot   dicots   did   different   diffuse   directly   discovered   discs   displacement   Displacement   displacing   Displacing   displayed   distances   Distribution   distribution   diverge   dl   doi   doing   dome   done   double   Download   dramatic   due   Due   each   Each   edu   effect   effort   either   Ellipsoid   ellipsoids   emphasize   employ   emulate   ended   ending   enhance   enhancing   ensure   environment   epidermal   especially   evasion   every   example   exits   expensive   experimentation   experimented   extra   extremely   fade   Fade   faint   fairly   far   fashion   Federl   few   fig8   file   Final   final   Finally   find   firstfin   five   flat   flower2a   foapproxeq   following   For   for   forced   format   forming   Forward   Foward   Fowler   fowler92collisionbased   fr   fractal   frequencies   Fresnel   from   From   ft   Fuhrer   function   Function   functions   further   fwdscatter   gateway   gave   generalized   generally   generate   generating   generation   Generation   Geometry   geometry   gets   Gimp   give   given   glu   Gnarled   Gnarling   go   good   gr   Graph   graphics   Graphics   Greenstein   growth   had   Hanrahan   harsh   heavily   Height   height   henrik   Henyey   henyey   higher   hope   horizontal   hour   how   however   Humphreys   hypocycloid   Hypocycloid   id   ieee   ieeexplore   iel5   If   ignoring   Illinois   imag   image   images   Images   imperfection   implement   Implementation   implemented   important   In   in   Inc   inclination   Increase   increment   indents   index   indicative   indices   infinite   Initial   initial   input   inside   Inspiration   instead   Instead   intend   intended   interacting   interactive   International   intersection   into   introduce   involved   irregular   isnumber   Iss   its   jagged   japan   Jason   Jensen   jitter   Johannes   Joseph   jpg   Jul   July   just   justification   Kaufmann   Kenmochi   kind   Knobs   know   knowledge   known   Kotani   Kreuger   Krueger   Kumar   ladder   Lagan   Lane   large   last   lateral   layered   layers   Leaf   leaf   learned   Leaves   left   length   lentical   less   level   Level   levels   lifelike   light   Lighting   lighting   lights   like   Lily   line   linearly   lines   link   Links   little   Location   long   look   looking   looks   loops   lot   lt   macro   made   main   make   many   map   mapping   Mapping   maps   match   material   Mathca   Mathematica   mathematica   mathematics   mathworld   maxima   mcb1   mcb2   me   means   mechanism   mentioned   mesh   meshes   method   micro   microfacets   middle   Mod   Model   model   modeling   Modeling   modified   modify   modules   more   More   Morgan   most   much   Multiresolution   must   my   N02   natural   Natural   nature   needed   netlike   new   New   next   Next   nice   Ninth   No   nodes   Noise   noise   normals   Note   Notice   number   Number   numerical   object   observed   of   off   offset   on   One   one   only   onto   open   Open   Oppenheimer   opted   or   order   oriented   originating   other   otherwise   out   output   overall   overlay   Overview   own   Pads   Pages   paper   parabolic   paraboloid   Paraboloid   parallel   parameters   Parameters   part   parts   pass   passing   pattern   patterngrid   patterns   pbrt   pdf   penetrate   penetrates   Penn   per   percurrent   perspective   Perspective   Perturbation   perturbation   Petal   petal   petals   Petals   Petals1   Peter   Pham   Pharr   phase   Phyllotaxis   physical   Physically   pic   pick   picker   picture   pistil   placement   plain   plan   plane   Plane   Plant   plant   plants   plugin   plus   png   point   polar   poor   portal   portion   position   positioning   possess   possibly   pp   ppham   precludes   predecessor   preliminary   present   Press   prevent   Previous   primary   Primary   prior   Priscilla   probabilities   probability   Probability   problem   procedural   Procedural   procedurally   Proceedings   Processing   produces   product   productions   prohibitively   Project   projects   prominently   Properties   properties   Proportional   Prototyping   prototyping   provide   Prunus   Prusinkiewicz   Przemyslaw   psu   Publications   Publishers   quick   quicker   radially   radiance   Radius   radius   random   randomized   ranges   ranging   Ranjitha   Rapid   ratios   reach   Real   real   realism   realistic   reality   recreated   recursion   Reduce   reflect   reflectance   reflected   Reflection   reflection   refraction   related   relatively   relevant   Render   render   render10   render11   Rendering   rendering   replace   represent   resemble   resulting   ret   reticulate   rewriting   rings   roadblock   Rolland   rose   Rose   rotate   rotated   Rotation   Rotations   rotations   row   rules   Runions   running   runtime   sakura   Sakura   same   save   scale   scatter   scattered   Scattering   scattering   scopic   secondaries   secondary   sectioning   sections   segments   sepals   September   sequences   series   serrulata   setting   several   shader   shape   shaped   shapes   sharp   sig   significantly   silky   similar   simulate   simulation   since   Since   sine   Single   single   singular   site   size   slices   slow   small   smaller   Smooth   smoothly   So   so   softness   solve   some   sometimes   soon   Source   source   space   specifically   specular   Spiral   spongy   spot   St   stacks   stamen   stanford   star   start   static   stays   stem   step   straight   straightforward   string   strip   structure   structures   study   sub   Sub   subdivisions   subsurf   Subsurface   subsurface   successor   such   Sudden   sum   summing   support   surface   surfaces   symbols   Synthetic   system   systems   Tachino   take   takes   Team   technical   technique   techniques   Techniques   Terado   Tertiary   test   Texture   texture   texturing   than   that   The   the   their   them   then   Theory   these   they   thin   thinner   this   This   those   three   through   time   times   to   together   Tom   too   took   Top   top   trans   Trans   transform   translate   Translation   translucency   translucent   transmitted   transparency   transport   tree   Tree   tree1   tree2   tree3   tree4   tree5   tree6   tree7   tree8   trees   Triangle   triangle   True   true   trunk   Trunk   try   turned   tweak   tweaking   tweaks   two   type   typical   ucsd   unexpected   uniform   uniformly   unique   unless   until   up   upcurving   upper   use   used   using   usually   utility   values   variance   varied   varies   Vein   vein   veins   venation   version   vertex   vertical   vertices   visualization   visualized   Vol   vol   wait   Wang   wanted   was   We   we   Weber   weird   well   were   What   When   where   which   Wikipedia   will   With   with   within   without   wolfram   work   Worley   worth   worthwhile   would   Writeup   writing   wrote   yields   York   zip   zoom  

Clear message

    PriscillaPham/FinalProject

Project Writeup : Sakura ("Cherry Blossom")

Team

  • Tom Wang
  • Priscilla Pham

Inspiration Images

Overview

  • Sakura trees (also known as cherry blossom trees) are among the most beautiful trees in nature and also present a worthwhile rendering challenge. In addition, we will procedurally model blossom petals by using an adaptation of the rose curve. Finally, we intend to employ subsurface scattering on the petals to capture the realistic details of softness and faint translucency.

Tree Overview

  • I model the tree procedurally with a modified L-system (defined with probability distribution functions along each depth of recursion) using generalized cylinders. I then generate a per-cylinder displacement map based on the geometry of the cylinder to add natural bark perturbation, enhancing realism. Next, I overlay with a per-cylinder bump map to emulate the circular indents present in lentical bark. Finally, I texture map a cherry blossom bark onto each cylinder. I provide technical details of each component below.

Procedural Tree Generation - Tom

Source Code

code.cpp

L-system Background

  • An L-system is a parallel string rewriting system, in which a simulation begins with an initial string called the axiom, which consists of modules, or symbols with associated numerical parameters. In each step of the simulation, rewriting rules—or productions—replace all modules in the predecessor string by successor modules. The resulting string can be visualized as a series of commands that link nodes, represent rotations, and distances between nodes.

Probability Distribution Function Implementation

  • I model each part of the tree as generalized cylinders and control the look of the tree with the following parameters:
  • Bottom radius
  • Top radius
  • Height
  • 3D Rotation and Translation
  • Initial radius fade (how much smaller the start radius of a sub-branch is)
  • Final radius fade (how much smaller the end radius of a sub-branch is)
  • Gnarling (overall displacement for next cylinder in link)
  • Number of sub-branches
  • Location of sub-branches Each cylinder is composed of a mesh of vertices in triangle strip format - these vertices are oriented as 'slices' (subdivisions around the main axis of the cylinder) and 'stacks' (subdivisions along the main axis of the cylinder). I am using a heavily modified gluCylinder() approach. Parameters are defined to be within certain ranges, depending on the level of branching, and are chosen with a uniform probability distribution function. For example, the trunk defines:

Trunk

  • Trunk radius - [1.7, 2.0]
  • Trunk height - [4, 5] * Trunk radius
  • Initial Fade - [1, 1]
  • Final Fade - [.8, .9]
  • Branches - [2]
  • Location of branches - [Trunk height]

Branch

  • 1st Level Branch radius - Trunk's Top Radius
  • 1st Level Branch height - [4, 12] * radius
  • 1st Level Branch initial fade - 1
  • 1st Level Branch final fade - [.3, .8] (varies linearly to branch height)
  • Branches - [2, 3]
  • Location of branches - [.95 * branch height, branch height]

Sub-branch

  • Sub Branch radius - Previous branch top radius * initial fade
  • Sub Branch height - [6, 12] * radius

  • Sub Branch initial fade - 1 (for level <= 3), [.8, .9] (otherwise)

  • Sub Branch final fade - [.1, .6] (for level <= 3), [.1, .35] (for level 4), [.3, .5] (otherwise)

  • Branches - [2, 2], [3, 4], [2, 6], [1, 4] (for levels 3, 4, (5, 6), and 7)
  • Location of branches - [.5, .95]

    In order to generate the tree, I begin with the trunk and continue branching until I either reach a cutoff level (level == 7) or the branches become too small (radius < .01). This technique is implemented as described in Oppenheimer's paper [10]. A few more details involved adding discs to either end of the cylinder to make them closed cylinders, creating a probability distribution for arbitrary rotations in 3D space, sectioning 3D space so that each branch gets its own portion to try to prevent against branch intersection (a true intersection test would be nice, but too expensive), modeling the vertical inclination of trees as described in Weber's paper [11], and calculating PDF parameters to ensure the tree stays within a desired bounds (also mentioned in [11]). The images below demonstrate my tweaking of PDF parameters to match the desired ratios for realistic cherry blossom trees.

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

Procedural Bump and Displacement Mapping - Tom

In order to better simulate the natural bumpiness of trees in reality, it became important to introduce displacement maps to change the physical geometry of vertices on the generalized cylinders as well as bump maps to change lighting normals and emphasize 'rings' of depth indicative of lentical bark. I first attempted to implement this inside a vertex shader using a texture as the source for normals and displacement and soon discovered that I needed to know the geometry related to each vertex to achieve the desired effect. Displacing too much would make small branches look weird and displacing too little would affect the trunk.

Instead, I chose to solve this problem by creating procedural displacement maps per branch - these maps look like random noise ranging uniformly from [-branch_radius/4, branch_radius/4]. Also, I create procedural bump maps per branch - these maps look like different frequencies of horizontal lines, each row has a random probability of generating a line and probabilities for the offset and length of this line. When applied to the tree, the bump map looks like circular rings.

I intended to also implement procedural texture mapping in the same fashion but discovered that PBRT only takes a single texture as input for triangle meshes. This means that I could not achieve a per-cylinder effect as I had done prior (I used OpenGL to modify the vertices and surface normals before I output to PBRT) unless I created an extremely large texture and had each cylinder index into a different portion of the texture. I did not have time to implement this before the rendering competition and was forced to use a static texture of a cherry tree.

Below is a picture of the tree with displacement mapping.

Natural Bark Perturbation With Displacement Mapping

OpenGL Application for Rapid Prototyping - Tom

Since PBRT doesn't allow for camera controls in real-time without doing another rendering pass, I wanted a much quicker prototyping environment to tweak my many parameters. I opted to go with OpenGL and defined a fairly comprehensive application that allowed me to rotate, zoom, translate, change perspective, generate a new tree, and output to PBRT file at runtime. This turned out to save me a lot of time overall since small tweaks on PBRT were prohibitively slow. I ended up writing a quick file utility that would output an OpenGL triangle strip into a PBRT triangle mesh with normals, texture coordinates, and indices defined.

Finally, the last work left was to tweak the image, find a good tree model, and pick a backdrop.

Ninth Render (backdrop)

Ninth Render (different model)

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 Geometry (Priscilla)

The blossom is constructed from plane curves that most closely resemble the shapes of 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 hypocycloid :

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. This final version of the model took more than an hour for Mathematica to render and would sometimes abort in the middle. If the increment step were decreased, the crinkles became sharp and jagged instead of smoothly curving. The final product was well worth the wait but the rendering effort was an unexpected roadblock.

The following is a Mathematica model of the sepals made of the hypocycloid with similar parabolic upcurving, 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 at the base 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, the plan was to generate randomized veins on the petal (all originating from the center) with a jitter transform, vertex noise, and/or Worley cellular texturing (procedural). According to one paper that this would have been based on, "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] This could possibly have been done with l-systems, although a different kind from the one used for the tree branches. Due to time constraints, however, this was not applied.

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.

[8]

Petals resemble thin surfaces, and their cross-sections can be described by open contours. We hope to apply this and other plant biology knowledge to enhance the appearance of the sakura petals.

Petal SSS

I wrote a new petal material plugin to PBRT, which added the BxDF per Hanrahan and Krueger [4]. Note that in the diagram above of the cellular layers of petals was significantly less and thinner than the leaf diagram that the paper mentioned, so we can take this as a justification of using the first order approximation method. The radiance is computed 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 and the Fresnel coefficients, calculate the BRDF and the BTDF. In this case the input values were around an index of refraction of 1.37 for the material, 1 for air, 3.8 for sig_a, 50 for sig_f, .15 for depth, 50 for g.

For the phase function we can use the Henyey-Greenstein approximation given in the paper:

Backscatter radiance:

Forward scatter radiance:

:

Foward scatter ignoring singular values:

For setting the initial specular and diffuse values I used a color picker in The Gimp on the model image. I added extra reflectance with microfacets to find the look that needed. What could have been done further is to look into the properties of the layers given in the Kotani[8] paper and apply the algorithm in a similar fashion to the leaf in the Hanrahan/Kreuger[4] paper.

Download the relevant source and preliminary projects -> here.

Final Single Sakura Blossom

One Blossom Next to Tree

Final Image

Links

Recent