SIMD look-at functions

SIMD+LookAt.swift

import simd

/// Creates a 4x4 matrix that orients the +Z axis in the direction of `at`, and the
/// +Y axis toward `up`.
func simd_look(at: SIMD3<Float>, up: SIMD3<Float> = SIMD3<Float>(0, 1, 0)) -> simd_float4x4 {
    let zAxis = normalize(at)
    let xAxis = normalize(cross(up, zAxis))
    let yAxis = normalize(cross(zAxis, xAxis))
    
    return simd_float4x4(
        SIMD4(xAxis, w: 0),
        SIMD4(yAxis, w: 0),
        SIMD4(zAxis, w: 0),
        SIMD4(0, 0, 0, 1)
    )
}

/// Creates a 4x4 matrix that positions the origin at `from`, orienting the +Z axis
/// so it points at `at`, and the +Y axis in the direction of `up`.
func simd_look(at: SIMD3<Float>, from: SIMD3<Float>, up: SIMD3<Float> = SIMD3<Float>(0, 1, 0)) -> simd_float4x4 {
    let zAxis = normalize(at - from)
    let xAxis = normalize(cross(up, zAxis))
    let yAxis = normalize(cross(zAxis, xAxis))
    
    return simd_float4x4(
        SIMD4(xAxis, w: 0),
        SIMD4(yAxis, w: 0),
        SIMD4(zAxis, w: 0),
        SIMD4(from, 1)
    )
}