向量投影证明_证明投影的第二条性质

https://stackoverflow.com/questions/52339320/unity-shader-hlsl-equivalent-of-vector3-projectonplane
a 在 b 上的投影

感觉向量还是这样写好看


mathmatica

Dot[{1，0} , {-1，0}]    // 点乘   是一个数
{1，0} x {-1，0}			// 叉乘   是一个向量
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// If your plane normal vector is normalized:

inline float3 projectOnPlane( float3 vec, float3 normal )
{
    return vec - normal * dot( vec, normal );
}
// If it's not:

inline float3 projectOnPlane( float3 vec, float3 normal )
{
    return vec - normal * ( dot( vec, normal ) / dot( normal, normal ) );
}
// Same formula, depending on GPU model & driver version can be either faster or slower:

inline float3 projectOnPlane( float3 v, float3 n )
{
    float3 r;
    r.x = n.y * n.y * v.x + n.z * n.z * v.x - n.x * n.y * v.y - n.x * n.z * v.z;
    r.y = n.x * n.x * v.y - n.x * n.y * v.x - n.y * n.z * v.z + n.z * n.z * v.y;
    r.z = n.x * n.x * v.z - n.x * n.z * v.x + n.y * n.y * v.z - n.y * n.z * v.y;
    return r / dot(n, n);
}
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