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coordsys.go
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coordsys.go
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// Copyright 2014 The Azul3D Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package lmath
import (
"fmt"
"math"
)
// CoordSys represents an specific coordinate system.
type CoordSys uint8
// RightHanded tells whether this coordinate system is right-handed.
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) RightHanded() bool {
switch c {
case CoordSysZUpRight:
return true
case CoordSysYUpRight:
return true
case CoordSysZUpLeft:
return false
case CoordSysYUpLeft:
return false
}
panic(fmt.Sprintf("RightHanded(): Invalid coordinate system %d", c))
}
// LeftHanded is short for:
// !cs.RightHanded()
func (c CoordSys) LeftHanded() bool {
return !c.RightHanded()
}
const (
// Invalid coordinate system
CoordSysInvalid CoordSys = iota
// Z up axis, right handed coordinate system
CoordSysZUpRight
// Y up axis, right handed coordinate system
CoordSysYUpRight
// Z up axis, left handed coordinate system
CoordSysZUpLeft
// Y up axis, left handed coordinate system
CoordSysYUpLeft
)
// Up returns the up vector for the given coordinate system
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) Up() Vec3 {
switch c {
case CoordSysZUpRight:
return Vec3{0, 0, 1}
case CoordSysZUpLeft:
return Vec3{0, 0, 1}
case CoordSysYUpRight:
return Vec3{0, 1, 0}
case CoordSysYUpLeft:
return Vec3{0, 1, 0}
}
panic(fmt.Sprintf("Up(): Invalid coordinate system %d", c))
}
// Right returns the right vector for the given coordinate system
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) Right() Vec3 {
return Vec3{1, 0, 0}
}
// Forward returns the forward vector for the given coordinate system
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) Forward() Vec3 {
switch c {
case CoordSysZUpRight:
return Vec3{0, 1, 0}
case CoordSysZUpLeft:
return Vec3{0, -1, 0}
case CoordSysYUpRight:
return Vec3{0, 0, -1}
case CoordSysYUpLeft:
return Vec3{0, 0, 1}
}
panic(fmt.Sprintf("Forward(): Invalid coordinate system %d", c))
}
// Down returns the down vector for the given coordinate system
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) Down() Vec3 {
return c.Up().Inverse()
}
// Left returns the left vector for the given coordinate system
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) Left() Vec3 {
return c.Right().Inverse()
}
// Back returns the back vector for the given coordinate system
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) Back() Vec3 {
return c.Forward().Inverse()
}
// RightFrontUp returns an vector that is described by it's right, forward, and
// up components in whatever way the specified coordinate system represents
// that vector.
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) RightFrontUp(right, forward, up float64) Vec3 {
var vz, vy float64
switch c {
case CoordSysYUpRight:
vz = -forward
vy = up
case CoordSysYUpLeft:
vz = forward
vy = up
case CoordSysZUpRight:
vy = forward
vz = up
case CoordSysZUpLeft:
vy = -forward
vz = up
default:
panic(fmt.Sprintf("Forward(): Invalid coordinate system %d", c))
}
return Vec3{right, vy, vz}
}
// ConvertMat3 returns a matrix that transforms from the indicated coordinate
// system, to the coordinate system specified.
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) ConvertMat3(to CoordSys) Mat3 {
switch c {
case CoordSysZUpLeft:
switch to {
case CoordSysZUpLeft:
return Mat3Identity
case CoordSysYUpLeft:
return Mat3ZToYUp
case CoordSysZUpRight:
return Mat3FlipY
case CoordSysYUpRight:
return Mat3LZToRY
}
case CoordSysYUpLeft:
switch to {
case CoordSysZUpLeft:
return Mat3YToZUp
case CoordSysYUpLeft:
return Mat3Identity
case CoordSysZUpRight:
return Mat3LYToRZ
case CoordSysYUpRight:
return Mat3FlipZ
}
case CoordSysZUpRight:
switch to {
case CoordSysZUpLeft:
return Mat3FlipY
case CoordSysYUpLeft:
return Mat3LZToRY
case CoordSysZUpRight:
return Mat3Identity
case CoordSysYUpRight:
return Mat3ZToYUp
}
case CoordSysYUpRight:
switch to {
case CoordSysZUpLeft:
return Mat3LYToRZ
case CoordSysYUpLeft:
return Mat3FlipZ
case CoordSysZUpRight:
return Mat3YToZUp
case CoordSysYUpRight:
return Mat3Identity
}
}
panic(fmt.Sprintf("ConvertMat3(): Invalid coordinate system %d / %d", c, to))
}
// ConvertMat4 returns a matrix that transforms from the indicated coordinate
// system, to the coordinate system specified.
// A panic will occur if the coordinate system is invalid.
func (c CoordSys) ConvertMat4(to CoordSys) Mat4 {
switch c {
case CoordSysZUpLeft:
switch to {
case CoordSysZUpLeft:
return Mat4Identity
case CoordSysYUpLeft:
return Mat4ZToYUp
case CoordSysZUpRight:
return Mat4FlipY
case CoordSysYUpRight:
return Mat4LZToRY
}
case CoordSysYUpLeft:
switch to {
case CoordSysZUpLeft:
return Mat4YToZUp
case CoordSysYUpLeft:
return Mat4Identity
case CoordSysZUpRight:
return Mat4LYToRZ
case CoordSysYUpRight:
return Mat4FlipZ
}
case CoordSysZUpRight:
switch to {
case CoordSysZUpLeft:
return Mat4FlipY
case CoordSysYUpLeft:
return Mat4LZToRY
case CoordSysZUpRight:
return Mat4Identity
case CoordSysYUpRight:
return Mat4ZToYUp
}
case CoordSysYUpRight:
switch to {
case CoordSysZUpLeft:
return Mat4LYToRZ
case CoordSysYUpLeft:
return Mat4FlipZ
case CoordSysZUpRight:
return Mat4YToZUp
case CoordSysYUpRight:
return Mat4Identity
}
}
panic(fmt.Sprintf("ConvertMat4(): Invalid coordinate system %d / %d", c, to))
}
// SphereToCart converts the Vec2{inclination, azimuth} point on a sphere of
// the given radius to cartesian coordinates and returns it.
//
// It is implemented according to:
// http://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates
func SphereToCart(r float64, p Vec2) Vec3 {
return Vec3{
X: r * math.Sin(p.X) * math.Cos(p.Y),
Y: r * math.Sin(p.X) * math.Sin(p.Y),
Z: r * math.Cos(p.X),
}
}
// CartToSphere converts the point in cartesian coordinate space, p, into
// spherical coordinates in the form of Vec3{radiys, inclination, azimuth} and
// returns it.
//
// It is implemented according to:
// http://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates
func CartToSphere(p Vec3) Vec3 {
r := p.Length()
i := math.Acos(p.Z / r)
a := math.Atan(p.Y / p.X)
return Vec3{r, i, a}
}