113 lines
3 KiB
Swift
113 lines
3 KiB
Swift
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// MathUtils.swift
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// Matrix and vector utilities for the viewport camera.
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import simd
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enum MathUtils {
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// MARK: - Projection
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static func perspective(
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fovYRadians fov: Float,
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aspect: Float,
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near: Float,
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far: Float
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) -> simd_float4x4 {
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let y = 1.0 / tanf(fov * 0.5)
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let x = y / aspect
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let z = far / (near - far)
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return simd_float4x4(columns: (
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SIMD4<Float>(x, 0, 0, 0),
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SIMD4<Float>(0, y, 0, 0),
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SIMD4<Float>(0, 0, z, -1),
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SIMD4<Float>(0, 0, z * near, 0)
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))
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}
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// MARK: - View
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static func lookAt(
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eye: SIMD3<Float>,
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center: SIMD3<Float>,
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up: SIMD3<Float>
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) -> simd_float4x4 {
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let f = normalize(center - eye)
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let s = normalize(cross(f, up))
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let u = cross(s, f)
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return simd_float4x4(columns: (
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SIMD4<Float>(s.x, u.x, -f.x, 0),
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SIMD4<Float>(s.y, u.y, -f.y, 0),
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SIMD4<Float>(s.z, u.z, -f.z, 0),
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SIMD4<Float>(-dot(s, eye), -dot(u, eye), dot(f, eye), 1)
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))
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}
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// MARK: - Model transforms
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static func translation(_ t: SIMD3<Float>) -> simd_float4x4 {
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var m = matrix_identity_float4x4
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m.columns.3 = SIMD4<Float>(t.x, t.y, t.z, 1)
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return m
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}
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static func scale(_ s: SIMD3<Float>) -> simd_float4x4 {
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return simd_float4x4(diagonal: SIMD4<Float>(s.x, s.y, s.z, 1))
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}
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static func rotationX(_ angle: Float) -> simd_float4x4 {
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let c = cosf(angle)
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let s = sinf(angle)
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return simd_float4x4(columns: (
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SIMD4<Float>(1, 0, 0, 0),
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SIMD4<Float>(0, c, s, 0),
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SIMD4<Float>(0, -s, c, 0),
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SIMD4<Float>(0, 0, 0, 1)
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))
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}
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static func rotationY(_ angle: Float) -> simd_float4x4 {
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let c = cosf(angle)
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let s = sinf(angle)
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return simd_float4x4(columns: (
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SIMD4<Float>( c, 0, s, 0),
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SIMD4<Float>( 0, 1, 0, 0),
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SIMD4<Float>(-s, 0, c, 0),
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SIMD4<Float>( 0, 0, 0, 1)
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))
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}
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static func rotationZ(_ angle: Float) -> simd_float4x4 {
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let c = cosf(angle)
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let s = sinf(angle)
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return simd_float4x4(columns: (
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SIMD4<Float>( c, s, 0, 0),
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SIMD4<Float>(-s, c, 0, 0),
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SIMD4<Float>( 0, 0, 1, 0),
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SIMD4<Float>( 0, 0, 0, 1)
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))
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}
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static func normalMatrix(from model: simd_float4x4) -> simd_float4x4 {
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let upper3x3 = simd_float3x3(
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model.columns.0.xyz,
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model.columns.1.xyz,
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model.columns.2.xyz
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)
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let inv = upper3x3.inverse.transpose
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return simd_float4x4(columns: (
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SIMD4<Float>(inv.columns.0, 0),
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SIMD4<Float>(inv.columns.1, 0),
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SIMD4<Float>(inv.columns.2, 0),
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SIMD4<Float>(0, 0, 0, 1)
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))
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}
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}
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// MARK: - SIMD helpers
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extension SIMD4 where Scalar == Float {
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var xyz: SIMD3<Float> { .init(x, y, z) }
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}
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