122 lines
3 KiB
Go
122 lines
3 KiB
Go
package main
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import (
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"math"
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)
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type Vector3 struct {
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X, Y, Z float64
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}
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func (u Vector3) GetColor(p Vector3) Vector3 {
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return u
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}
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func (u Vector3) Add(v Vector3) Vector3 {
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return Vector3{u.X + v.X, u.Y + v.Y, u.Z + v.Z}
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}
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func (u Vector3) Neg() Vector3 {
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return Vector3{-u.X, -u.Y, -u.Z}
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}
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func (u Vector3) Sub(v Vector3) Vector3 {
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return u.Add(v.Neg())
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}
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func (u Vector3) Scale(a float64) Vector3 {
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return Vector3{a * u.X, a * u.Y, a * u.Z}
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}
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func (u Vector3) Dot(v Vector3) float64 {
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return u.X*v.X + u.Y*v.Y + u.Z*v.Z
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}
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func (u Vector3) Cross(v Vector3) Vector3 {
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return Vector3{u.Y*v.Z - u.Z*v.Y, u.Z*v.X - u.X*v.Z, u.X*v.Y - u.Y*v.X}
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}
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func (u Vector3) LengthSquared() float64 {
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return u.Dot(u)
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}
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func (u Vector3) Length() float64 {
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return math.Sqrt(u.LengthSquared())
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}
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func (u Vector3) Normalized() Vector3 {
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return u.Scale(1.0 / u.Length())
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}
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func (u Vector3) Round() Vector3 {
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round := math.Round
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return Vector3{round(u.X), round(u.Y), round(u.Z)}
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}
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func (u Vector3) Abs() Vector3 {
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abs := math.Abs
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return Vector3{abs(u.X), abs(u.Y), abs(u.Z)}
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}
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func (u Vector3) Max(x float64) Vector3 {
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return Vector3{max(u.X, x), max(u.Y, x), max(u.Z, x)}
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}
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func (u Vector3) Min(x float64) Vector3 {
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return Vector3{min(u.X, x), min(u.Y, x), min(u.Z, x)}
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}
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// i incident, n normal. Both vector should be normalized
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func Reflect(i Vector3, n Vector3) Vector3 {
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y := i.Dot(n)
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return (n.Scale(2 * y)).Sub(i)
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}
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// Todo : Refract
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// Rodrigues' rotation formula. rotVector should be normalized
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func Rotate(u Vector3, rotVector Vector3, angle float64) Vector3 {
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cos, sin := math.Cos(angle), math.Sin(angle)
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vec1 := u.Scale(cos)
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vec2 := rotVector.Cross(u).Scale(sin)
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vec3 := rotVector.Scale(rotVector.Dot(u) * (1 - cos))
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return vec1.Add(vec2).Add(vec3)
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}
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func Mix(u Vector3, v Vector3, k float64) Vector3 {
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l := (1 - k)
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return Vector3{u.X*l + v.X*k, u.Y*l + v.Y*k, u.Z*l + v.Z*k}
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}
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func (v Vector3) Unpack() (float64, float64, float64) {
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return v.X, v.Y, v.Z
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}
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// Return position, and units vectors of spherical into cartesian coords (r, theta, phi) units vecs
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func (v Vector3) SphericalToCartesian() (Vector3, Vector3, Vector3, Vector3) {
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p, theta, phi := v.Unpack()
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cos_theta, sin_theta := math.Cos(theta), math.Sin(theta)
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cos_phi, sin_phi := math.Cos(phi), math.Sin(phi)
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cart_pos := Vector3{p * cos_theta * cos_phi, p * sin_theta * sin_phi, p * cos_theta}
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unit_vec_r := Vector3{sin_theta * cos_phi, sin_theta * cos_phi, cos_theta}
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unit_vec_theta := Vector3{cos_theta * cos_phi, cos_theta * sin_phi, -sin_theta}
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unit_vec_phi := Vector3{-sin_phi, cos_phi, 0}
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return cart_pos, unit_vec_r, unit_vec_theta, unit_vec_phi
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}
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// Others maths thingies
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func Clamp(x float64, a float64, b float64) float64 {
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return min(max(x, a), b)
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}
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func (v Vector3) Clamp(a float64, b float64) Vector3 {
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x, y, z := v.Unpack()
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x, y, z = Clamp(x, a, b), Clamp(y, a, b), Clamp(z, a, b)
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return Vector3{x, y, z}
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}
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func SmoothStep(x float64, a float64, b float64) float64 {
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x = Clamp((x-a)/(b-a), 0, 1)
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return x * x * (3.0 - 2.0*x)
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}
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