versorc-math 0.1.1

Low-level Clifford Geometric Algebra, Versor Operators, and High-Dimensional Matrix Reductions
Documentation 
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#version 450

// ============================================================================
// VERSORC VULKAN CGA COMPUTE PRIMITIVE: CGA_TRANSFORM
// 3D Conformal Geometric Algebra Spherical Inversion & Conformal Versors
// License: Apache-2.0
// ============================================================================

layout(local_size_x = 64, local_size_y = 1, local_size_z = 1) in;

layout(push_constant) uniform CgaPushConstants {
    uint num_points;
    uint op_type; // 0: Spherical Inversion, 1: Dilation, 2: Translation
    float sphere_cx;
    float sphere_cy;
    float sphere_cz;
    float sphere_radius;
    float param_lambda; // Dilation factor or translation dx
    float param_dy;
    float param_dz;
    uint _pad0;
    uint _pad1;
    uint _pad2;
} pc;

layout(std430, binding = 0) readonly buffer PointsIn {
    vec4 in_pts[];
};

layout(std430, binding = 1) writeonly buffer PointsOut {
    vec4 out_pts[];
};

void main() {
    uint idx = gl_GlobalInvocationID.x;
    if (idx >= pc.num_points) {
        return;
    }

    vec3 p = in_pts[idx].xyz;
    vec3 center = vec3(pc.sphere_cx, pc.sphere_cy, pc.sphere_cz);

    if (pc.op_type == 0u) {
        // Spherical Inversion across sphere (center, radius)
        vec3 d = p - center;
        float dist_sq = dot(d, d);
        float r_sq = pc.sphere_radius * pc.sphere_radius;
        if (dist_sq > 1e-12) {
            vec3 p_inv = center + (r_sq / dist_sq) * d;
            out_pts[idx] = vec4(p_inv, 1.0);
        } else {
            out_pts[idx] = vec4(center, 0.0); // Point at infinity
        }
    } else if (pc.op_type == 1u) {
        // Conformal Dilation
        out_pts[idx] = vec4(p * pc.param_lambda, 1.0);
    } else {
        // Conformal Translation
        vec3 shift = vec3(pc.param_lambda, pc.param_dy, pc.param_dz);
        out_pts[idx] = vec4(p + shift, 1.0);
    }
}