## 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 aboutÂ 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:

- foreach triangle
**T**in the mesh - find the area
**A**and density**D**of**T** - ifÂ
**D*****A*** factor > 1 then - choose a point
**Y**inside**T**using barycentric coordinates - 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.

- The average of the density of the points situated on the Bresenham’s lines of triangle
**T**

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.

## Generating geometry

In this post I will present how I implemented the `GenerateGeometry`

function from the iFurMaterial interface. This function can be split in two big parts: guide hair and hair strands generation.

**Generating guide hairs**

These guide hairs will be used only for physics simulation and as reference for the hair strands. So they will not be rendered, except maybe for debug purpose.

In order to generate guide hairs the base mesh, the mesh on which fur will grow, will be used. If there are enough vertices, guide hairs will be attach to each point of every vertex. If not, the mesh will either be tessellated using a CS function, or by implementing the same technique used to generate hair strands from guide hairs. The only important thing here is to also have a vertex buffer (triangle buffer actually) for these guide hairs, and not just an index buffer (a vector to store them).

Unless any physics model is specify (ropes or so), guide hairs will grow having the direction of the vertex normal and a length specify via a heightmap.

**Generating hair strands**

This is where the guide hairs triangle buffer will be used. For each such triangle, based on a density map, hair strands will be generated. In order to get any number of points inside a triangle, as random distributed as possibly, barycentric coordinates will be used.

If we look closely at the above picture, we see that we can generate a point Y, in a triangle ABC, just by `Y = bA * A + bB * B + bC * C`

, where `bA + bB + bC = 1`

. And randomly choosing the barycentric coordinates is not tough at all: `bA = random (0,1), bB = random (0,1) * (1 - bA), bC = 1 - bA - bB`

.

The interesting thing here is that these barycentric coordinates can also be used for setting the whole hair strand (not just the base point), and even the UV coordinates for the density map.

**Updating Geometry**

All hair strands need to be updated even if there is no physics model involved.

The iFurPhysicsControl interface will update guide hairs, and after this, hair strands will be regenerated every time. Even if no physics interface is specify the hair strands still need to be regenerated because they are represented as triangle strips and they need to always face the camera. This can be done be taking into account that the vertex tangent has to be perpendicular to the eye direction.

csVector3 firstPoint = furMaterial->hairStrands.Get(x).controlPoints[y];

csVector3 secondPoint = furMaterial->hairStrands.Get(x).controlPoints[y + 1];

csVector3 tangent;

csMath3::CalcNormal(`tangent`

`, firstPoint, secondPoint, tc.GetOrigin());`

`tangent`

`.Normalize();`

strip = furMaterial->strandWidth * `tangent`

`;`

The reason why I used solid geometry instead of lines is that vertices support both textures and shaders.

**The result**

Here is a picture of some generated hair strands, with no physics model specified (hair grows on vertex normal direction).