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1954 lines (1572 loc) · 55.8 KB
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//
// VectorMath.swift
// VectorMath
//
// Version 0.9
//
// Created by Janne Raiskila, based on VectorMath created by Nick Lockwood
// on 24/11/2014. Copyright (c) 2014-2015 Nick Lockwood and Janne Raiskila
//
// Distributed under the permissive zlib License
// Get the latest version from here:
//
// https://github.com/acdx/VectorMath
//
// This software is provided 'as-is', without any express or implied
// warranty. In no event will the authors be held liable for any damages
// arising from the use of this software.
//
// Permission is granted to anyone to use this software for any purpose,
// including commercial applications, and to alter it and redistribute it
// freely, subject to the following restrictions:
//
// 1. The origin of this software must not be misrepresented; you must not
// claim that you wrote the original software. If you use this software
// in a product, an acknowledgment in the product documentation would be
// appreciated but is not required.
//
// 2. Altered source versions must be plainly marked as such, and must not be
// misrepresented as being the original software.
//
// 3. This notice may not be removed or altered from any source distribution.
//
import Foundation
typealias Scalar = Double
//MARK: Protocols
protocol Vector2Type {
var __x: Scalar { get }
var __y: Scalar { get }
}
protocol Vector3Type {
var __x: Scalar { get }
var __y: Scalar { get }
var __z: Scalar { get }
}
protocol Vector4Type {
var __x: Scalar { get }
var __y: Scalar { get }
var __z: Scalar { get }
var __w: Scalar { get }
}
protocol QuaternionType: Vector4Type {}
protocol Matrix3Type {
var __m11: Scalar { get }
var __m12: Scalar { get }
var __m13: Scalar { get }
var __m21: Scalar { get }
var __m22: Scalar { get }
var __m23: Scalar { get }
var __m31: Scalar { get }
var __m32: Scalar { get }
var __m33: Scalar { get }
}
protocol Matrix4Type {
var __m11: Scalar { get }
var __m12: Scalar { get }
var __m13: Scalar { get }
var __m14: Scalar { get }
var __m21: Scalar { get }
var __m22: Scalar { get }
var __m23: Scalar { get }
var __m24: Scalar { get }
var __m31: Scalar { get }
var __m32: Scalar { get }
var __m33: Scalar { get }
var __m34: Scalar { get }
var __m41: Scalar { get }
var __m42: Scalar { get }
var __m43: Scalar { get }
var __m44: Scalar { get }
}
protocol InstantiableVector2Type: Vector2Type {
init(__x: Scalar, __y: Scalar)
}
protocol InstantiableVector3Type: Vector3Type {
init(__x: Scalar, __y: Scalar, __z: Scalar)
}
protocol InstantiableVector4Type: Vector4Type {
init(__x: Scalar, __y: Scalar, __z: Scalar, __w: Scalar)
}
protocol InstantiableQuaternionType: QuaternionType, InstantiableVector4Type {}
protocol InstantiableMatrix3Type: Matrix3Type {
init(
__m11: Scalar, __m12: Scalar, __m13: Scalar,
__m21: Scalar, __m22: Scalar, __m23: Scalar,
__m31: Scalar, __m32: Scalar, __m33: Scalar
)
}
protocol InstantiableMatrix4Type: Matrix4Type {
init(
__m11: Scalar, __m12: Scalar, __m13: Scalar, __m14: Scalar,
__m21: Scalar, __m22: Scalar, __m23: Scalar, __m24: Scalar,
__m31: Scalar, __m32: Scalar, __m33: Scalar, __m34: Scalar,
__m41: Scalar, __m42: Scalar, __m43: Scalar, __m44: Scalar
)
}
//MARK: Extensions
extension Vector2Type {
var lengthSquared: Scalar {
return __x * __x + __y * __y
}
var length: Scalar {
return sqrt(lengthSquared)
}
func toArray() -> [Scalar] {
return [__x, __y]
}
func dot(v: Vector2Type) -> Scalar {
return __x * v.__x + __y * v.__y
}
func cross(v: Vector2Type) -> Scalar {
return __x * v.__y - __y * v.__x
}
func angleWith(v: Vector2Type) -> Scalar {
if self.vector2IsEqual(v) {
return 0
}
let t1 = __Vector2(self).normalized()
let t2 = __Vector2(v).normalized()
let cross = t1.cross(t2)
let dot = max(-1, min(1, t1.dot(t2)))
return atan2(cross, dot)
}
func vector2IsEqual(v: Vector2Type) -> Bool {
return __x == v.__x && __y == v.__y
}
func vector2IsApproxEqual(v: Vector2Type) -> Bool {
return __x ~~= v.__x && __y ~~= v.__y
}
}
extension Vector3Type {
var lengthSquared: Scalar {
return __x * __x + __y * __y + __z * __z
}
var length: Scalar {
return sqrt(lengthSquared)
}
func toArray() -> [Scalar] {
return [__x, __y, __z]
}
func dot(v: Vector3Type) -> Scalar {
return __x * v.__x + __y * v.__y + __z * v.__z
}
func xy<T: InstantiableVector2Type>() -> T {
return T(__x: __x, __y: __y)
}
func xz<T: InstantiableVector2Type>() -> T {
return T(__x: __x, __y: __z)
}
func yz<T: InstantiableVector2Type>() -> T {
return T(__x: __y, __y: __z)
}
func vector3IsEqual(v: Vector3Type) -> Bool {
return __x == v.__x && __y == v.__y && __z == v.__z
}
func vector3IsApproxEqual(v: Vector3Type) -> Bool {
return __x ~~= v.__x && __y ~~= v.__y && __z ~~= v.__z
}
}
extension Vector4Type {
var lengthSquared: Scalar {
return __x * __x + __y * __y + __z * __z + __w * __w
}
var length: Scalar {
return sqrt(lengthSquared)
}
func toArray() -> [Scalar] {
return [__x, __y, __z, __w]
}
func dot(v: Vector4Type) -> Scalar {
return __x * v.__x + __y * v.__y + __z * v.__z + __w * v.__w
}
func xyz<T: InstantiableVector3Type>() -> T {
return T(__x: __x, __y: __y, __z: __z)
}
func xy<T: InstantiableVector2Type>() -> T {
return T(__x: __x, __y: __y)
}
func xz<T: InstantiableVector2Type>() -> T {
return T(__x: __x, __y: __z)
}
func yz<T: InstantiableVector2Type>() -> T {
return T(__x: __y, __y: __z)
}
func vector4IsEqual(v: Vector4Type) -> Bool {
return __x == v.__x && __y == v.__y && __z == v.__z && __w == v.__w
}
func vector4IsApproxEqual(v: Vector4Type) -> Bool {
return __x ~~= v.__x && __y ~~= v.__y && __z ~~= v.__z && __w ~~= v.__w
}
}
extension QuaternionType {
var pitch: Scalar {
return atan2(2 * (__y * __z + __w * __x), __w * __w - __x * __x - __y * __y + __z * __z)
}
var yaw: Scalar {
return asin(-2 * (__x * __z - __w * __y))
}
var roll: Scalar {
return atan2(2 * (__x * __y + __w * __z), __w * __w + __x * __x - __y * __y - __z * __z)
}
func toPitchYawRoll() -> (pitch: Scalar, yaw: Scalar, roll: Scalar) {
return (pitch, yaw, roll)
}
func toAxisAngle<T: InstantiableVector4Type>() -> T {
let xyzVector: __Vector3 = xyz()
let scale = xyzVector.length
if scale ~~= 0 || scale ~~= .twoPi {
return T(__x: 0, __y: 0, __z: 1, __w: 0)
} else {
return T(__x: __x / scale, __y: __y / scale, __z: __z / scale, __w: acos(__w) * 2)
}
}
func quaternionIsEqual(v: QuaternionType) -> Bool {
return vector4IsEqual(v)
}
func quaternionIsApproxEqual(v: QuaternionType) -> Bool {
return vector4IsApproxEqual(v)
}
}
extension Matrix3Type {
func toArray() -> [Scalar] {
return [__m11, __m12, __m13, __m21, __m22, __m23, __m31, __m32, __m33]
}
var determinant: Scalar {
return (__m11 * __m22 * __m33 + __m12 * __m23 * __m31 + __m13 * __m21 * __m32)
- (__m13 * __m22 * __m31 + __m11 * __m23 * __m32 + __m12 * __m21 * __m33)
}
func matrix3IsEqual(m: Matrix3Type) -> Bool {
return
__m11 == m.__m11 && __m12 == m.__m12 && __m13 == m.__m13 &&
__m21 == m.__m21 && __m22 == m.__m22 && __m23 == m.__m23 &&
__m31 == m.__m31 && __m32 == m.__m32 && __m33 == m.__m33
}
func matrix3IsApproxEqual(m: Matrix3Type) -> Bool {
return
__m11 ~~= m.__m11 && __m12 ~~= m.__m12 && __m13 ~~= m.__m13 &&
__m21 ~~= m.__m21 && __m22 ~~= m.__m22 && __m23 ~~= m.__m23 &&
__m31 ~~= m.__m31 && __m32 ~~= m.__m32 && __m33 ~~= m.__m33
}
}
extension Matrix4Type {
func toArray() -> [Scalar] {
return [
__m11, __m12, __m13, __m14,
__m21, __m22, __m23, __m24,
__m31, __m32, __m33, __m34,
__m41, __m42, __m43, __m44
]
}
private func determinantForAdjugate(m: Matrix4Type) -> Scalar {
return __m11 * m.__m11 + __m12 * m.__m21 + __m13 * m.__m31 + __m14 * m.__m41
}
var determinant: Scalar {
let copy = __Matrix4(self)
return determinantForAdjugate(copy.adjugate)
}
func matrix4IsEqual(m: Matrix4Type) -> Bool {
return
__m11 == m.__m11 && __m12 == m.__m12 && __m13 == m.__m13 && __m14 == m.__m14 &&
__m21 == m.__m21 && __m22 == m.__m22 && __m23 == m.__m23 && __m24 == m.__m24 &&
__m31 == m.__m31 && __m32 == m.__m32 && __m33 == m.__m33 && __m34 == m.__m34 &&
__m41 == m.__m41 && __m42 == m.__m42 && __m43 == m.__m43 && __m44 == m.__m44
}
func matrix4IsApproxEqual(m: Matrix4Type) -> Bool {
return
__m11 ~~= m.__m11 && __m12 ~~= m.__m12 && __m13 ~~= m.__m13 && __m14 ~~= m.__m14 &&
__m21 ~~= m.__m21 && __m22 ~~= m.__m22 && __m23 ~~= m.__m23 && __m24 ~~= m.__m24 &&
__m31 ~~= m.__m31 && __m32 ~~= m.__m32 && __m33 ~~= m.__m33 && __m34 ~~= m.__m34 &&
__m41 ~~= m.__m41 && __m42 ~~= m.__m42 && __m43 ~~= m.__m43 && __m44 ~~= m.__m44
}
}
extension InstantiableVector2Type {
var inverse: Self {
return -self
}
func normalized() -> Self {
let lengthSquared = self.lengthSquared
if lengthSquared ~~= 0 || lengthSquared ~~= 1 {
return self
}
return self / sqrt(lengthSquared)
}
func rotatedBy(radians: Scalar) -> Self {
let cs = cos(radians)
let sn = sin(radians)
return Self(__x: __x * cs - __y * sn, __y: __x * sn + __y * cs)
}
func rotatedBy(radians: Scalar, around pivot: Vector2Type) -> Self {
return (self - pivot).rotatedBy(radians) + pivot
}
func interpolatedWith(v: Vector2Type, t: Scalar) -> Self {
return self + (v - self) * t
}
}
extension InstantiableVector3Type {
var inverse: Self {
return -self
}
func cross(v: Vector3Type) -> Self {
return Self(
__x: __y * v.__z - __z * v.__y,
__y: __z * v.__x - __x * v.__z,
__z: __x * v.__y - __y * v.__x
)
}
func normalized() -> Self {
let lengthSquared = self.lengthSquared
if lengthSquared ~~= 0 || lengthSquared ~~= 1 {
return self
}
return self / sqrt(lengthSquared)
}
func interpolatedWith(v: Vector3Type, t: Scalar) -> Self {
return self + (v - self) * t
}
}
extension InstantiableVector4Type {
var inverse: Self {
return -self
}
func normalized() -> Self {
let lengthSquared = self.lengthSquared
if lengthSquared ~~= 0 || lengthSquared ~~= 1 {
return self
}
return self / sqrt(lengthSquared)
}
func interpolatedWith(v: Vector4Type, t: Scalar) -> Self {
return self + (v - self) * t
}
}
extension InstantiableQuaternionType {
func interpolatedWith(q: QuaternionType, t: Scalar) -> Self {
let dot = max(-1, min(1, self.dot(q)))
if dot ~~= 1 {
return (self + (q - self) * t).normalized()
}
let theta = acos(dot) * t
let t1 = self * cos(theta)
let t2 = (q - (self * dot)).normalized() * sin(theta)
return t1 + t2
}
init(__axisAngle axisAngle: Vector4Type) {
let r = axisAngle.__w * 0.5
let scale = sin(r)
let xyzVector: __Vector3 = axisAngle.xyz()
let a = xyzVector * scale
self.init(__x: a.__x, __y: a.__y, __z: a.__z, __w: cos(r))
}
init(__pitch pitch: Scalar, __yaw yaw: Scalar, __roll roll: Scalar) {
let sy = sin(yaw * 0.5)
let cy = cos(yaw * 0.5)
let sz = sin(roll * 0.5)
let cz = cos(roll * 0.5)
let sx = sin(pitch * 0.5)
let cx = cos(pitch * 0.5)
self.init(
__x: cy * cz * cx - sy * sz * sx,
__y: sy * sz * cx + cy * cz * sx,
__z: sy * cz * cx + cy * sz * sx,
__w: cy * sz * cx - sy * cz * sx
)
}
init(__rotationMatrix m: Matrix4Type) {
let diagonal = m.__m11 + m.__m22 + m.__m33 + 1
if diagonal ~~= 0 {
let scale = sqrt(diagonal) * 2
self.init(
__x: (m.__m32 - m.__m23) / scale,
__y: (m.__m13 - m.__m31) / scale,
__z: (m.__m21 - m.__m12) / scale,
__w: 0.25 * scale
)
} else if m.__m11 > max(m.__m22, m.__m33) {
let scale = sqrt(1 + m.__m11 - m.__m22 - m.__m33) * 2
self.init(
__x: 0.25 * scale,
__y: (m.__m21 + m.__m12) / scale,
__z: (m.__m13 + m.__m31) / scale,
__w: (m.__m32 - m.__m23) / scale
)
} else if m.__m22 > m.__m33 {
let scale = sqrt(1 + m.__m22 - m.__m11 - m.__m33) * 2
self.init(
__x: (m.__m21 + m.__m12) / scale,
__y: 0.25 * scale,
__z: (m.__m32 + m.__m23) / scale,
__w: (m.__m13 - m.__m31) / scale
)
} else {
let scale = sqrt(1 + m.__m33 - m.__m11 - m.__m22) * 2
self.init(
__x: (m.__m13 + m.__m31) / scale,
__y: (m.__m32 + m.__m23) / scale,
__z: 0.25 * scale,
__w: (m.__m21 - m.__m12) / scale
)
}
}
}
extension InstantiableMatrix3Type {
var adjugate: Self {
return Self(
__m11: __m22 * __m33 - __m23 * __m32,
__m12: __m13 * __m32 - __m12 * __m33,
__m13: __m12 * __m23 - __m13 * __m22,
__m21: __m23 * __m31 - __m21 * __m33,
__m22: __m11 * __m33 - __m13 * __m31,
__m23: __m13 * __m21 - __m11 * __m23,
__m31: __m21 * __m32 - __m22 * __m31,
__m32: __m12 * __m31 - __m11 * __m32,
__m33: __m11 * __m22 - __m12 * __m21
)
}
var transpose: Self {
return Self(
__m11: __m11, __m12: __m21, __m13: __m31,
__m21: __m12, __m22: __m22, __m23: __m32,
__m31: __m13, __m32: __m23, __m33: __m33
)
}
var inverse: Self {
return adjugate * (1 / determinant)
}
func interpolatedWith(m: Matrix3Type, t: Scalar) -> Self {
return Self(
__m11: __m11 + (m.__m11 - __m11) * t,
__m12: __m12 + (m.__m12 - __m12) * t,
__m13: __m13 + (m.__m13 - __m13) * t,
__m21: __m21 + (m.__m21 - __m21) * t,
__m22: __m22 + (m.__m22 - __m22) * t,
__m23: __m23 + (m.__m23 - __m23) * t,
__m31: __m31 + (m.__m31 - __m31) * t,
__m32: __m32 + (m.__m32 - __m32) * t,
__m33: __m33 + (m.__m33 - __m33) * t
)
}
init(__scale scale: Vector2Type) {
self.init(
__m11: scale.__x, __m12: 0, __m13: 0,
__m21: 0, __m22: scale.__y, __m23: 0,
__m31: 0, __m32: 0, __m33: 1
)
}
init(__translation translation: Vector2Type) {
self.init(
__m11: 1, __m12: 0, __m13: 0,
__m21: 0, __m22: 1, __m23: 0,
__m31: translation.__x, __m32: translation.__y, __m33: 1
)
}
init(__rotation radians: Scalar) {
let cs = cos(radians)
let sn = sin(radians)
self.init(
__m11: cs, __m12: sn, __m13: 0,
__m21: -sn, __m22: cs, __m23: 0,
__m31: 0, __m32: 0, __m33: 1
)
}
}
extension InstantiableMatrix4Type {
var adjugate: Self {
return Self(
__m11: (__m22 * __m33 * __m44 - __m22 * __m34 * __m43) +
(-__m32 * __m23 * __m44 + __m32 * __m24 * __m43) +
(__m42 * __m23 * __m34 - __m42 * __m24 * __m33),
__m12: (-__m12 * __m33 * __m44 + __m12 * __m34 * __m43) +
(__m32 * __m13 * __m44 - __m32 * __m14 * __m43) +
(-__m42 * __m13 * __m34 + __m42 * __m14 * __m33),
__m13: (__m12 * __m23 * __m44 - __m12 * __m24 * __m43) +
(-__m22 * __m13 * __m44 + __m22 * __m14 * __m43) +
(__m42 * __m13 * __m24 - __m42 * __m14 * __m23),
__m14: (-__m12 * __m23 * __m34 + __m12 * __m24 * __m33) +
(__m22 * __m13 * __m34 - __m22 * __m14 * __m33) +
(-__m32 * __m13 * __m24 + __m32 * __m14 * __m23),
__m21: (-__m21 * __m33 * __m44 + __m21 * __m34 * __m43) +
(__m31 * __m23 * __m44 - __m31 * __m24 * __m43) +
(-__m41 * __m23 * __m34 + __m41 * __m24 * __m33),
__m22: (__m11 * __m33 * __m44 - __m11 * __m34 * __m43) +
(-__m31 * __m13 * __m44 + __m31 * __m14 * __m43) +
(__m41 * __m13 * __m34 - __m41 * __m14 * __m33),
__m23: (-__m11 * __m23 * __m44 + __m11 * __m24 * __m43) +
(__m21 * __m13 * __m44 - __m21 * __m14 * __m43) +
(-__m41 * __m13 * __m24 + __m41 * __m14 * __m23),
__m24: (__m11 * __m23 * __m34 - __m11 * __m24 * __m33) +
(-__m21 * __m13 * __m34 + __m21 * __m14 * __m33) +
(__m31 * __m13 * __m24 - __m31 * __m14 * __m23),
__m31: (__m21 * __m32 * __m44 - __m21 * __m34 * __m42) +
(-__m31 * __m22 * __m44 + __m31 * __m24 * __m42) +
(__m41 * __m22 * __m34 - __m41 * __m24 * __m32),
__m32: (-__m11 * __m32 * __m44 + __m11 * __m34 * __m42) +
(__m31 * __m12 * __m44 - __m31 * __m14 * __m42) +
(-__m41 * __m12 * __m34 + __m41 * __m14 * __m32),
__m33: (__m11 * __m22 * __m44 - __m11 * __m24 * __m42) +
(-__m21 * __m12 * __m44 + __m21 * __m14 * __m42) +
(__m41 * __m12 * __m24 - __m41 * __m14 * __m22),
__m34: (-__m11 * __m22 * __m34 + __m11 * __m24 * __m32) +
(__m21 * __m12 * __m34 - __m21 * __m14 * __m32) +
(-__m31 * __m12 * __m24 + __m31 * __m14 * __m22),
__m41: (-__m21 * __m32 * __m43 + __m21 * __m33 * __m42) +
(__m31 * __m22 * __m43 - __m31 * __m23 * __m42) +
(-__m41 * __m22 * __m33 + __m41 * __m23 * __m32),
__m42: (__m11 * __m32 * __m43 - __m11 * __m33 * __m42) +
(-__m31 * __m12 * __m43 + __m31 * __m13 * __m42) +
(__m41 * __m12 * __m33 - __m41 * __m13 * __m32),
__m43: (-__m11 * __m22 * __m43 + __m11 * __m23 * __m42) +
(__m21 * __m12 * __m43 - __m21 * __m13 * __m42) +
(-__m41 * __m12 * __m23 + __m41 * __m13 * __m22),
__m44: (__m11 * __m22 * __m33 - __m11 * __m23 * __m32) +
(-__m21 * __m12 * __m33 + __m21 * __m13 * __m32) +
(__m31 * __m12 * __m23 - __m31 * __m13 * __m22)
)
}
var transpose: Self {
return Self(
__m11: __m11, __m12: __m21, __m13: __m31, __m14: __m41,
__m21: __m12, __m22: __m22, __m23: __m32, __m24: __m42,
__m31: __m13, __m32: __m23, __m33: __m33, __m34: __m43,
__m41: __m14, __m42: __m24, __m43: __m34, __m44: __m44
)
}
var inverse: Self {
let adjugate = self.adjugate
let determinant = determinantForAdjugate(adjugate)
return adjugate * (1 / determinant)
}
init(__scale s: Vector3Type) {
self.init(
__m11: s.__x, __m12: 0, __m13: 0, __m14: 0,
__m21: 0, __m22: s.__y, __m23: 0, __m24: 0,
__m31: 0, __m32: 0, __m33: s.__z, __m34: 0,
__m41: 0, __m42: 0, __m43: 0, __m44: 1
)
}
init(__translation t: Vector3Type) {
self.init(
__m11: 1, __m12: 0, __m13: 0, __m14: 0,
__m21: 0, __m22: 1, __m23: 0, __m24: 0,
__m31: 0, __m32: 0, __m33: 1, __m34: 0,
__m41: t.__x, __m42: t.__y, __m43: t.__z, __m44: 1
)
}
init(__rotation axisAngle: Vector4Type) {
self.init(__quaternion: __Quaternion(axisAngle: axisAngle))
}
init(__quaternion q: QuaternionType) {
self.init(
__m11: 1 - 2 * (q.__y * q.__y + q.__z * q.__z), __m12: 2 * (q.__x * q.__y + q.__z * q.__w),
__m13: 2 * (q.__x * q.__z - q.__y * q.__w), __m14: 0,
__m21: 2 * (q.__x * q.__y - q.__z * q.__w), __m22: 1 - 2 * (q.__x * q.__x + q.__z * q.__z),
__m23: 2 * (q.__y * q.__z + q.__x * q.__w), __m24: 0,
__m31: 2 * (q.__x * q.__z + q.__y * q.__w), __m32: 2 * (q.__y * q.__z - q.__x * q.__w),
__m33: 1 - 2 * (q.__x * q.__x + q.__y * q.__y), __m34: 0,
__m41: 0, __m42: 0, __m43: 0, __m44: 1
)
}
init(__fovx fovx: Scalar, __fovy fovy: Scalar, __near near: Scalar, __far far: Scalar) {
self.init(__fovy: fovy, __aspect: fovx / fovy, __near: near, __far: far)
}
init(__fovx fovx: Scalar, __aspect aspect: Scalar, __near near: Scalar, __far far: Scalar) {
self.init(__fovy: fovx / aspect, __aspect: aspect, __near: near, __far: far)
}
init(__fovy fovy: Scalar, __aspect aspect: Scalar, __near near: Scalar, __far far: Scalar) {
let dz = far - near
assert(dz > 0, "far value must be greater than near")
assert(fovy > 0, "field of view must be nonzero and positive")
assert(aspect > 0, "aspect ratio must be nonzero and positive")
let r = fovy / 2
let cotangent = cos(r) / sin(r)
self.init(
__m11: cotangent / aspect, __m12: 0, __m13: 0, __m14: 0,
__m21: 0, __m22: cotangent, __m23: 0, __m24: 0,
__m31: 0, __m32: 0, __m33: -(far + near) / dz, __m34: -1,
__m41: 0, __m42: 0, __m43: -2 * near * far / dz, __m44: 0
)
}
init(__top top: Scalar, __right right: Scalar, __bottom bottom: Scalar, __left left: Scalar,
__near near: Scalar, __far far: Scalar) {
let dx = right - left
let dy = top - bottom
let dz = far - near
self.init(
__m11: 2 / dx, __m12: 0, __m13: 0, __m14: 0,
__m21: 0, __m22: 2 / dy, __m23: 0, __m24: 0,
__m31: 0, __m32: 0, __m33: -2 / dz, __m34: 0,
__m41: -(right + left) / dx, __m42: -(top + bottom) / dy, __m43: -(far + near) / dz, __m44: 1
)
}
}
//MARK: Vector2 operators
prefix func +<T: InstantiableVector2Type>(v: T) -> T {
return v
}
prefix func -<T: InstantiableVector2Type>(v: T) -> T {
return T(__x: -v.__x, __y: -v.__y)
}
func +<T: InstantiableVector2Type>(lhs: T, rhs: T) -> T {
return T(__x: lhs.__x + rhs.__x, __y: lhs.__y + rhs.__y)
}
func +<T: InstantiableVector2Type>(lhs: T, rhs: Vector2Type) -> T {
return T(__x: lhs.__x + rhs.__x, __y: lhs.__y + rhs.__y)
}
func +<T: InstantiableVector2Type>(lhs: Vector2Type, rhs: T) -> T {
return T(__x: lhs.__x + rhs.__x, __y: lhs.__y + rhs.__y)
}
func -<T: InstantiableVector2Type>(lhs: T, rhs: T) -> T {
return T(__x: lhs.__x - rhs.__x, __y: lhs.__y - rhs.__y)
}
func -<T: InstantiableVector2Type>(lhs: T, rhs: Vector2Type) -> T {
return T(__x: lhs.__x - rhs.__x, __y: lhs.__y - rhs.__y)
}
func -<T: InstantiableVector2Type>(lhs: Vector2Type, rhs: T) -> T {
return T(__x: lhs.__x - rhs.__x, __y: lhs.__y - rhs.__y)
}
func *<T: InstantiableVector2Type>(lhs: T, rhs: T) -> T {
return T(__x: lhs.__x * rhs.__x, __y: lhs.__y * rhs.__y)
}
func *<T: InstantiableVector2Type>(lhs: T, rhs: Vector2Type) -> T {
return T(__x: lhs.__x * rhs.__x, __y: lhs.__y * rhs.__y)
}
func *<T: InstantiableVector2Type>(lhs: Vector2Type, rhs: T) -> T {
return T(__x: lhs.__x * rhs.__x, __y: lhs.__y * rhs.__y)
}
func *<T: InstantiableVector2Type>(lhs: Scalar, rhs: T) -> T {
return T(__x: lhs * rhs.__x, __y: lhs * rhs.__y)
}
func *<T: InstantiableVector2Type>(lhs: T, rhs: Scalar) -> T {
return T(__x: lhs.__x * rhs, __y: lhs.__y * rhs)
}
func *<T: InstantiableVector2Type>(lhs: T, rhs: Matrix3Type) -> T {
return T(
__x: lhs.__x * rhs.__m11 + lhs.__y * rhs.__m21 + rhs.__m31,
__y: lhs.__x * rhs.__m12 + lhs.__y * rhs.__m22 + rhs.__m32
)
}
func *<T: InstantiableVector2Type>(lhs: Matrix3Type, rhs: T) -> T {
return rhs * lhs
}
func /<T: InstantiableVector2Type>(lhs: T, rhs: T) -> T {
return T(__x: lhs.__x / rhs.__x, __y: lhs.__y / rhs.__y)
}
func /<T: InstantiableVector2Type>(lhs: T, rhs: Vector2Type) -> T {
return T(__x: lhs.__x / rhs.__x, __y: lhs.__y / rhs.__y)
}
func /<T: InstantiableVector2Type>(lhs: Vector2Type, rhs: T) -> T {
return T(__x: lhs.__x / rhs.__x, __y: lhs.__y / rhs.__y)
}
func /<T: InstantiableVector2Type>(lhs: T, rhs: Scalar) -> T {
return T(__x: lhs.__x / rhs, __y: lhs.__y / rhs)
}
func +=<T: InstantiableVector2Type>(inout lhs: T, rhs: T) {
lhs = lhs + rhs
}
func +=<T: InstantiableVector2Type>(inout lhs: T, rhs: Vector2Type) {
lhs = lhs + rhs
}
func -=<T: InstantiableVector2Type>(inout lhs: T, rhs: T) {
lhs = lhs - rhs
}
func -=<T: InstantiableVector2Type>(inout lhs: T, rhs: Vector2Type) {
lhs = lhs - rhs
}
func *=<T: InstantiableVector2Type>(inout lhs: T, rhs: T) {
lhs = lhs * rhs
}
func *=<T: InstantiableVector2Type>(inout lhs: T, rhs: Vector2Type) {
lhs = lhs * rhs
}
func *=<T: InstantiableVector2Type>(inout lhs: T, rhs: Scalar) {
lhs = lhs * rhs
}
func *=<T: InstantiableVector2Type>(inout lhs: T, rhs: Matrix3Type) {
lhs = lhs * rhs
}
func /=<T: InstantiableVector2Type>(inout lhs: T, rhs: T) {
lhs = lhs / rhs
}
func /=<T: InstantiableVector2Type>(inout lhs: T, rhs: Vector2Type) {
lhs = lhs / rhs
}
func /=<T: InstantiableVector2Type>(inout lhs: T, rhs: Scalar) {
lhs = lhs / rhs
}
//MARK: Vector3 operators
prefix func +<T: InstantiableVector3Type>(v: T) -> T {
return v
}
prefix func -<T: InstantiableVector3Type>(v: T) -> T {
return T(__x: -v.__x, __y: -v.__y, __z: -v.__z)
}
func +<T: InstantiableVector3Type>(lhs: T, rhs: T) -> T {
return T(__x: lhs.__x + rhs.__x, __y: lhs.__y + rhs.__y, __z: lhs.__z + rhs.__z)
}
func +<T: InstantiableVector3Type>(lhs: T, rhs: Vector3Type) -> T {
return T(__x: lhs.__x + rhs.__x, __y: lhs.__y + rhs.__y, __z: lhs.__z + rhs.__z)
}
func +<T: InstantiableVector3Type>(lhs: Vector3Type, rhs: T) -> T {
return T(__x: lhs.__x + rhs.__x, __y: lhs.__y + rhs.__y, __z: lhs.__z + rhs.__z)
}
func -<T: InstantiableVector3Type>(lhs: T, rhs: T) -> T {
return T(__x: lhs.__x - rhs.__x, __y: lhs.__y - rhs.__y, __z: lhs.__z - rhs.__z)
}
func -<T: InstantiableVector3Type>(lhs: T, rhs: Vector3Type) -> T {
return T(__x: lhs.__x - rhs.__x, __y: lhs.__y - rhs.__y, __z: lhs.__z - rhs.__z)
}
func -<T: InstantiableVector3Type>(lhs: Vector3Type, rhs: T) -> T {
return T(__x: lhs.__x - rhs.__x, __y: lhs.__y - rhs.__y, __z: lhs.__z - rhs.__z)
}
func *<T: InstantiableVector3Type>(lhs: T, rhs: T) -> T {
return T(__x: lhs.__x * rhs.__x, __y: lhs.__y * rhs.__y, __z: lhs.__z * rhs.__z)
}
func *<T: InstantiableVector3Type>(lhs: T, rhs: Vector3Type) -> T {
return T(__x: lhs.__x * rhs.__x, __y: lhs.__y * rhs.__y, __z: lhs.__z * rhs.__z)
}
func *<T: InstantiableVector3Type>(lhs: Vector3Type, rhs: T) -> T {
return T(__x: lhs.__x * rhs.__x, __y: lhs.__y * rhs.__y, __z: lhs.__z * rhs.__z)
}
func *<T: InstantiableVector3Type>(lhs: Scalar, rhs: T) -> T {
return T(__x: lhs * rhs.__x, __y: lhs * rhs.__y, __z: lhs * rhs.__z)
}
func *<T: InstantiableVector3Type>(lhs: T, rhs: Scalar) -> T {
return T(__x: lhs.__x * rhs, __y: lhs.__y * rhs, __z: lhs.__z * rhs)
}
func *<T: InstantiableVector3Type>(lhs: T, rhs: Matrix3Type) -> T {
return T(
__x: lhs.__x * rhs.__m11 + lhs.__y * rhs.__m21 + lhs.__z * rhs.__m31,
__y: lhs.__x * rhs.__m12 + lhs.__y * rhs.__m22 + lhs.__z * rhs.__m32,
__z: lhs.__x * rhs.__m13 + lhs.__y * rhs.__m23 + lhs.__z * rhs.__m33
)
}
func *<T: InstantiableVector3Type>(lhs: T, rhs: Matrix4Type) -> T {
return T(
__x: lhs.__x * rhs.__m11 + lhs.__y * rhs.__m21 + lhs.__z * rhs.__m31 + rhs.__m41,
__y: lhs.__x * rhs.__m12 + lhs.__y * rhs.__m22 + lhs.__z * rhs.__m32 + rhs.__m42,
__z: lhs.__x * rhs.__m13 + lhs.__y * rhs.__m23 + lhs.__z * rhs.__m33 + rhs.__m43
)
}
func *<T: InstantiableVector3Type>(lhs: Matrix3Type, rhs: T) -> T {
return rhs * lhs
}
func *<T: InstantiableVector3Type>(lhs: Matrix4Type, rhs: T) -> T {
return rhs * lhs
}
func *<T: InstantiableVector3Type>(v: T, q: QuaternionType) -> T {
let qv: __Vector3 = q.xyz()
let uv = qv.cross(v)
let uuv = qv.cross(uv)
let sub = uv * 2 * q.__w
return v + sub + (uuv * 2)
}
func *<T: InstantiableVector3Type>(lhs: QuaternionType, rhs: T) -> T {
return rhs * lhs
}
func /<T: InstantiableVector3Type>(lhs: T, rhs: T) -> T {
return T(__x: lhs.__x / rhs.__x, __y: lhs.__y / rhs.__y, __z: lhs.__z / rhs.__z)
}
func /<T: InstantiableVector3Type>(lhs: T, rhs: Vector3Type) -> T {
return T(__x: lhs.__x / rhs.__x, __y: lhs.__y / rhs.__y, __z: lhs.__z / rhs.__z)
}
func /<T: InstantiableVector3Type>(lhs: Vector3Type, rhs: T) -> T {
return T(__x: lhs.__x / rhs.__x, __y: lhs.__y / rhs.__y, __z: lhs.__z / rhs.__z)
}
func /<T: InstantiableVector3Type>(lhs: T, rhs: Scalar) -> T {
return T(__x: lhs.__x / rhs, __y: lhs.__y / rhs, __z: lhs.__z / rhs)
}
func +=<T: InstantiableVector3Type>(inout lhs: T, rhs: T) {
lhs = lhs + rhs
}
func +=<T: InstantiableVector3Type>(inout lhs: T, rhs: Vector3Type) {
lhs = lhs + rhs
}
func -=<T: InstantiableVector3Type>(inout lhs: T, rhs: T) {
lhs = lhs - rhs
}
func -=<T: InstantiableVector3Type>(inout lhs: T, rhs: Vector3Type) {
lhs = lhs - rhs
}
func *=<T: InstantiableVector3Type>(inout lhs: T, rhs: T) {
lhs = lhs * rhs
}
func *=<T: InstantiableVector3Type>(inout lhs: T, rhs: Vector3Type) {
lhs = lhs * rhs
}
func *=<T: InstantiableVector3Type>(inout lhs: T, rhs: Scalar) {
lhs = lhs * rhs
}
func *=<T: InstantiableVector3Type>(inout lhs: T, rhs: Matrix3Type) {
lhs = lhs * rhs
}
func *=<T: InstantiableVector3Type>(inout lhs: T, rhs: Matrix4Type) {
lhs = lhs * rhs
}
func *=<T: InstantiableVector3Type>(inout lhs: T, rhs: QuaternionType) {
lhs = lhs * rhs
}
func /=<T: InstantiableVector3Type>(inout lhs: T, rhs: T) {
lhs = lhs / rhs
}
func /=<T: InstantiableVector3Type>(inout lhs: T, rhs: Vector3Type) {
lhs = lhs / rhs