Rotation matrix for Metal

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Apr 26, 2023

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func makeRotationMatrix(angleRadians: Float, axis: simd_float3) -> matrix_float4x4 {
    let normalizedAxis = normalize(axis)
    let cosAngle = cos(angleRadians)
    let sinAngle = sin(angleRadians)
    let oneMinusCosAngle = 1 - cosAngle
    
    let row0 = simd_float4(
        cosAngle + normalizedAxis.x * normalizedAxis.x * oneMinusCosAngle,
        normalizedAxis.x * normalizedAxis.y * oneMinusCosAngle - normalizedAxis.z * sinAngle,
        normalizedAxis.x * normalizedAxis.z * oneMinusCosAngle + normalizedAxis.y * sinAngle,
        0
    )
    
    let row1 = simd_float4(
        normalizedAxis.y * normalizedAxis.x * oneMinusCosAngle + normalizedAxis.z * sinAngle,
        cosAngle + normalizedAxis.y * normalizedAxis.y * oneMinusCosAngle,
        normalizedAxis.y * normalizedAxis.z * oneMinusCosAngle - normalizedAxis.x * sinAngle,
        0
    )
    
    let row2 = simd_float4(
        normalizedAxis.z * normalizedAxis.x * oneMinusCosAngle - normalizedAxis.y * sinAngle,
        normalizedAxis.z * normalizedAxis.y * oneMinusCosAngle + normalizedAxis.x * sinAngle,
        cosAngle + normalizedAxis.z * normalizedAxis.z * oneMinusCosAngle,
        0
    )
    
    let row3 = simd_float4(0, 0, 0, 1)
    
    let matrix = matrix_float4x4(rows: [row0, row1, row2, row3])
    return matrix
}

func makeQuaternionRotationMatrix(angleRadians: Float, axis: simd_float3) -> matrix_float4x4 {
    let normalizedAxis = normalize(axis)
    let halfAngle = angleRadians / 2
    let w = cos(halfAngle)
    let sinHalfAngle = sin(halfAngle)
    let x = sinHalfAngle * normalizedAxis.x
    let y = sinHalfAngle * normalizedAxis.y
    let z = sinHalfAngle * normalizedAxis.z
    
    let quaternion = simd_quatf(ix: x, iy: y, iz: z, r: w)
    let rotationMatrix = matrix_float4x4(quaternion)
    
    return rotationMatrix
}