Left-handed and right-handed perspective matrix for Metal

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Apr 26, 2023

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func matrix_perspective_left_hand(fovyRadians fovy: Float, aspectRatio: Float, nearZ: Float, farZ: Float) -> matrix_float4x4 {
    let ys = 1 / tanf(fovy * 0.5)
    let xs = ys / aspectRatio
    let zs = farZ / (nearZ - farZ)
    return matrix_float4x4.init(columns:(vector_float4(xs,  0, 0,   0),
                                         vector_float4( 0, ys, 0,   0),
                                         vector_float4( 0,  0, -zs, 1),
                                         vector_float4( 0,  0, zs * nearZ, 0)))
}

func makeLeftHandedPerspectiveMatrix(fovyRadians fovy: Float, aspectRatio: Float, nearZ near: Float, farZ far: Float) -> matrix_float4x4 {
    let yScale = 1 / tan(fovy / 2)
    let xScale = yScale / aspectRatio
    let zScale = far / (far - near)
    let wzScale = -zScale * near
    
    let matrix = matrix_float4x4([
        simd_float4(xScale, 0, 0, 0),
        simd_float4(0, yScale, 0, 0),
        simd_float4(0, 0, zScale, 1),
        simd_float4(0, 0, wzScale, 0)
    ])
    
    return matrix
}

func matrix_perspective_right_hand(fovyRadians fovy: Float, aspectRatio: Float, nearZ: Float, farZ: Float) -> matrix_float4x4 {
    let ys = 1 / tanf(fovy * 0.5)
    let xs = ys / aspectRatio
    let zs = farZ / (nearZ - farZ)
    return matrix_float4x4.init(columns:(vector_float4(xs,  0, 0,   0),
                                         vector_float4( 0, ys, 0,   0),
                                         vector_float4( 0,  0, zs, -1),
                                         vector_float4( 0,  0, zs * nearZ, 0)))
}

func makeRightHandedPerspectiveMatrix(fovyRadians fovy: Float, aspectRatio: Float, nearZ near: Float, farZ far: Float) -> matrix_float4x4 {
    let yScale = 1 / tan(fovy / 2)
    let xScale = yScale / aspectRatio
    let zScale = far / (far - near)
    let wzScale = -zScale * near
    
    let matrix = matrix_float4x4([
        simd_float4(xScale, 0, 0, 0),
        simd_float4(0, yScale, 0, 0),
        simd_float4(0, 0, -zScale, -1),
        simd_float4(0, 0, wzScale, 0)
    ])
    
    return matrix
}