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Archive for July, 2010

UV Maps

In this post I will explain how I managed to set some properties like length and density for the hair mesh.

The challenge here was to adapt a well-known technique and use it for these particular features. This technique consisted of UV maps, and was used for Krystal’s skull mesh (the picture from the left), whose UV map looks like this (in the right):

The length map

This is actually very similar to your usual heightmap, especially used for terrains and such, but it is UV mapped.

The data from this image is interpreted also similar to that of a heightmap, but it sets the length of the hair strands in that vicinity and not the height of the mesh, hence the name length map instead of density map.

And an example for a bangs hairstyle is the following UV map (left), having the result from right when applied to Krystal:

The density map

Although the density map looks similar to the other UV map, the length map, getting data from it, is done quite differently.

This is caused by the fact that data from this image is used to generate new data (geometry) as opposed to just refine existent geometry, which is the case with the length map.

Generating new geometry based on a UV map is also used in adaptive tessellation, but there the map used is a displacement map also having information about  the direction of the newly created meshes.

For this algorithm to work the mesh has to be composed of triangles and an UV density map has to be specified. The steps of the algorithm are as follows:

  1. foreach triangle T in the mesh
  2.   find the area A and density D of T
  3.   if  D * A * factor > 1 then
  4.     choose a point Y inside T using barycentric coordinates
  5.     delete T and create 3 other triangles based on Y and T

The only things uncommon are choosing a point using barycenctric coordinates and finding out the density of a triangle based on an UV map. Regarding the barycentric coordinates you can check out one of my previous posts, where I also explained this technique when used to generate hair strands. Finding the density of a triangle based on the density map is not hard either, and I tried three ways of doing this, all based on the fact that UV coordinates are known for A, B and C, the points of triangle T.

  • The average of A, B and C density

Although this approach evaluates just three points, it gives good enough results when there are plenty triangles to begin with and the UV map is at a lower resolution. Also applying a Gaussian filter on the image at the begging of the algorithm helps.

Actually I got to admit that this is not my idea, but I heard it from a colleague that used it for a real-time adaptive tessellation application. The main advantage of this approach is that it represents a compromise between speed and information analyzed. Also to improve this way of getting the density of a triangle convolution matrices can be used in order to obtain information from the vicinity of the currently analyzed point as well.

  • The sum of all points density in the triangle T

Even though this might be the most obvious way to get the density of a triangle, generating all points inside of a triangle is not that easy. In order to do this I used the ever mentioned barycentric coordinates, but this time they weren’t generated random at all. Having in mind that the area of a triangle, which covers the whole surface of this polygon, is the base multiplied by height and divided by two, generating the first two barycentric coordinates along these lines seemed a good solution. The only problem is that the points further away from the base are analyzed more times (no division by two means passing points in this area more than one time), so doing this operation three times (one time for each base) and then getting the average, gives a very close approximation of the triangle density. Because I do this operation only at the begging I used this last method in the fur plugin implementation, being the best choice regarding the amount of information analyzed.

Next you can see Krystal having just a few hair strands on the top of her skull:

Other UV maps

UV maps can also be used to set various other information about a mesh, such as: the contour of a mesh, which vertices are more important or setting different materials/colors on different hair strands.

I already used UV maps to determine the contour of the geometry and to determine some pivots vertices (as guide ropes). Those pictures look like this, left is the contour:

I haven’t use UV maps to generate various colors for different hair strands, but I have in mind two approaches, and after implementing them I will write another post. However I think my next post will be about the LOD system for the fur plugin which is currently under development.

Halfway there

The 16th July midterm deadline just passed and I haven’t posted in a while, so I am going to make a short presentation about what I have done so far and what is still to be done for this GSoC project.

Done:

  • Generated geometry – iFurMaterial
  • Animated geometry – iFurPhysicsControl
  • Written specific shaders – iFurStrandGenerator

TODO’s:

  • LOD – working on it
  • Shadows – at least receiving shadows from other objects
  • Blender integration – if there is any time left

Recently I have finished adding support for density and height maps, and I will soon write how I have done this. I think that the way in which hair strands are generated, based on the density map, is quite general and could be used even for an adaptive tessellation project, so I will try to write my next post about this as soon as possible.

Until then I leave you with this video, showing more or less what I have implemented so far (YouTubeHD):

Categories: Crystal Space Tags: ,

Marschner Shader Part III

This is the last part of the three post regarding the Marschner shader. I will explain how to efficiently make the shader for this model, how to add ambient and diffuse lighting and at the end of the post I will also give source code for generating Marschner lookup textures and a video showing the results I had in CS.

Lookup Textures

Because there are too many computations done in M and N functions to be put in the pixel shader, the best optimization is to use lookup textures, that need to be updated as rarely as possible.

We can easily observe that apart from the constants defined in Table 1 ( page 8 ) from Marschner’s paper, the M function only depends on q i and q r , and N on q d and f d. Although this might seem a good optimization at first, taking into account that all these angles must be computed from inverse trigonometric functions, such as acos and asin, which aren’t fast at all, indexing the lookup textures directly by cos and sin sounds a better idea.

The way in which sinus and cosinus values can be computed for all these angles can be found in GPU Gems 2, Chapter 23:

  • sin q i = (light · Tangent),
  • sin q o = (eye · Tangent).
  • lightPerp = light – (light · tangent) x tangent,
  • eyePerp = eye – (eye · tangent) x tangent.
  • cos f d = (eyePerp · lightPerp) x ((eyePerp · eyePerp) x (lightPerp · lightPerp))-0.5

As for the cos q d if we observe that q d depends on q i and q r then we figure out that we can use a channel from the lookup texture indexed by the sins of these two angles.

The easiest way to build these two textures is to make a lookup texture for M, having MR, MTT, MTRT and cos q d, and a lookup texture for N. However, in the original paper NTT and NTRT each have three channels, but they can be reduced to only one channel if we consider the absorption to have one channel as well.

These are the lookup textures obtained with my first implementation of the Marschner project:

Ambient and diffuse lighting

The Marschner model only specifies the specular component for lighting, so in order to obtain nice visual effects, both ambient and diffuse lighting were added to this model.

I used the lighting from the Nalu Demo, presented in detail in one of my previous posts:

/* Compute diffuse lighting with phi-dependent component */
float diffuse = sqrt(max(0.0001, 1 - uv1.x * uv1.x));

/* Pass colors */
float4 diffuseColor;
diffuseColor.rgb = diffuse * objColor.rgb * DiffuseCol;
diffuseColor.a = objColor.a;
float3 ambientColor;
ambientColor = objColor.rgb * AmbientCol;

float3 lighting = (( M.r * N.r + M.g * N.g + M.b * N.b ) / (cos_qd * cos_qd));
lighting += diffuseColor.rgb;

OUT.xyz = lighting + diffuseColor.rgb * 0.2 + IN.AmbientColor;

Source code

Here you can find the first version of my Marschner C# Project, which generates the lookup textures needed for a shader similar to the one presented in the Nalu Demo post.

There are still some things that can be improved, but I plan to release another version for that, as soon as I get a chance. Until then feel free to improve the project yourself.

These are the two adjustments done to the original model, as described in Marschner:

  1. The absorption is specify by only one channel.
  2. Instead of the standard NTRT component, the simplify version was used.

You can find more information in the README, INSTALL and LICENSE files from the archive.

Demo

Next you can see the effects this shader has on Krystal’s hair. If you want to play with the application yourself checkout the hair branch from CS main repository.