Writing Bone Matrix Calculations in GLSL

In GLSL (OpenGL Shading Language), bone matrix calculations are typically used for skeletal animation, where the transformation of a model is driven by a skeleton’s bones. To handle this, you must calculate the transformation matrices for each bone in the skeleton and then apply these matrices to the vertices of the model.

Here’s a basic breakdown of how you can implement bone matrix calculations in GLSL.

1. Understanding the Bone Matrix

A bone matrix consists of the transformation that applies to the vertices of the model from the bone’s local space to world space. It is composed of a combination of rotation, scaling, and translation. Typically, each vertex will be influenced by one or more bones, and you’ll need to calculate a weighted sum of the transformations for each vertex.

2. Skinning

In skeletal animation, skinning refers to the process of applying the transformations of bones to the vertices of the mesh. Two popular methods for skinning are linear blend skinning (LBS) and dual quaternion skinning. Here, we will focus on Linear Blend Skinning (also known as skeletal animation).

Linear Blend Skinning involves transforming each vertex using a weighted sum of bone transformations. The formula for transforming a vertex $v$ in world space is:

Where:

• $v$ is the vertex in model space.

• $w_i$ is the weight of the influence of bone $i$ on the vertex.

• $M_i$ is the transformation matrix of bone $i$.

• The sum is done over all the bones influencing the vertex.

3. GLSL Code for Bone Matrix Calculation

Vertex Shader

Here is an example of a vertex shader that handles bone matrix calculations:

glsl
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#version 450

layout(location = 0) in vec3 inPosition;    // Vertex position
layout(location = 1) in vec3 inNormal;      // Vertex normal
layout(location = 2) in ivec4 inBoneIDs;    // Bone indices for this vertex
layout(location = 3) in vec4 inBoneWeights; // Weights for each bone

uniform mat4 model;                      // Model matrix (transforming object to world space)
uniform mat4 view;                       // View matrix (camera transformation)
uniform mat4 projection;                 // Projection matrix (for perspective)
uniform mat4 boneMatrices[100];          // Bone transformation matrices

out vec3 fragNormal;                     // Pass normal to fragment shader
out vec3 fragPosition;                   // Pass position to fragment shader

void main()
{
    mat4 boneTransform = mat4(0.0);  // Initialize an identity matrix to hold the weighted sum

    // Calculate the weighted sum of bone transforms
    for (int i = 0; i < 4; ++i) {
        if (inBoneWeights[i] > 0.0) {
            boneTransform += inBoneWeights[i] * boneMatrices[inBoneIDs[i]];
        }
    }

    // Apply bone transformation to the vertex position
    vec4 worldPosition = boneTransform * vec4(inPosition, 1.0);

    // Transform the normal by the bone matrix (ignoring translation part)
    mat3 normalMatrix = mat3(boneTransform); // 3x3 matrix excludes translation part
    fragNormal = normalize(normalMatrix * inNormal);

    // Apply the final transformations (model -> view -> projection)
    fragPosition = vec3(view * model * worldPosition); 
    gl_Position = projection * vec4(fragPosition, 1.0);
}

Explanation of the Vertex Shader:

1. Inputs:

   • inPosition: The position of the vertex.

   • inNormal: The normal of the vertex (for lighting calculations).

   • inBoneIDs: The indices of the bones influencing this vertex.

   • inBoneWeights: The weights associated with each bone for this vertex.

2. Uniforms:

   • boneMatrices[100]: An array of matrices for each bone. This is typically passed from the CPU-side application.

   • model, view, projection: Transformation matrices to move the model from object space to screen space.

3. Bone Matrix Calculation:

   • The shader calculates a weighted sum of bone matrices, which transform the vertex position. Each bone’s matrix is multiplied by the weight for that bone.

   • boneMatrices[inBoneIDs[i]]: Accesses the transformation matrix for each bone based on the bone’s ID.

4. Normal Transformation:

   • The normal is transformed similarly to the position, but only the rotation and scale parts of the matrix are applied (using a 3×3 matrix).

5. Final Transformation:

   • The vertex is then transformed by the model, view, and projection matrices to move it to the correct place in screen space.

Fragment Shader

Typically, the fragment shader will use the transformed normal to calculate lighting or other effects. Here’s a simple fragment shader that uses the normal and the vertex position:

glsl
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#version 450

in vec3 fragNormal;    // Normal passed from vertex shader
in vec3 fragPosition;  // Position passed from vertex shader

out vec4 FragColor;    // Output color

void main()
{
    // Simple diffuse lighting based on the light direction
    vec3 lightDir = normalize(vec3(1.0, 1.0, 1.0)); // Light source direction
    float diff = max(dot(fragNormal, lightDir), 0.0);  // Diffuse lighting

    // Set fragment color based on normal and lighting
    FragColor = vec4(diff, diff, diff, 1.0);
}

4. Passing Bone Data from CPU to GPU

On the CPU side, you would need to send the bone matrices and weights to the shader. You would typically calculate the bone transformations on the CPU, then pass them to the shader as uniform variables (like boneMatrices[100]).

5. Conclusion

This GLSL code shows a basic way to handle bone matrix calculations using linear blend skinning. For more complex scenarios, you could incorporate additional optimizations, such as using dual quaternion skinning for better visual quality, or implementing more advanced lighting and texture mapping techniques for the final render.