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vec.go
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vec.go
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package ms3
import math "github.com/chewxy/math32"
// Vec is a 3D vector.
type Vec struct {
X, Y, Z float32
}
// Add returns the vector sum of p and q.
func Add(p, q Vec) Vec {
return Vec{
X: p.X + q.X,
Y: p.Y + q.Y,
Z: p.Z + q.Z,
}
}
// Sub returns the vector sum of p and -q.
func Sub(p, q Vec) Vec {
return Vec{
X: p.X - q.X,
Y: p.Y - q.Y,
Z: p.Z - q.Z,
}
}
// Scale returns the vector p scaled by f.
func Scale(f float32, p Vec) Vec {
return Vec{
X: f * p.X,
Y: f * p.Y,
Z: f * p.Z,
}
}
// Dot returns the dot product p·q.
func Dot(p, q Vec) float32 {
return p.X*q.X + p.Y*q.Y + p.Z*q.Z
}
// Cross returns the cross product p×q.
func Cross(p, q Vec) Vec {
return Vec{
p.Y*q.Z - p.Z*q.Y,
p.Z*q.X - p.X*q.Z,
p.X*q.Y - p.Y*q.X,
}
}
// Rotate returns a new vector, rotated by alpha around the provided axis.
// func Rotate(p Vec, alpha float32, axis Vec) Vec {
// return NewRotation(alpha, axis).Rotate(p)
// }
// Norm returns the Euclidean norm of p
//
// |p| = sqrt(p_x^2 + p_y^2 + p_z^2).
func Norm(p Vec) float32 {
return math.Hypot(p.X, math.Hypot(p.Y, p.Z))
}
// Norm2 returns the Euclidean squared norm of p
//
// |p|^2 = p_x^2 + p_y^2 + p_z^2.
func Norm2(p Vec) float32 {
return p.X*p.X + p.Y*p.Y + p.Z*p.Z
}
// Unit returns the unit vector colinear to p.
// Unit returns {NaN,NaN,NaN} for the zero vector.
func Unit(p Vec) Vec {
if p.X == 0 && p.Y == 0 && p.Z == 0 {
return Vec{X: math.NaN(), Y: math.NaN(), Z: math.NaN()}
}
return Scale(1/Norm(p), p)
}
// Cos returns the cosine of the opening angle between p and q.
func Cos(p, q Vec) float32 {
return Dot(p, q) / (Norm(p) * Norm(q))
}
// Divergence returns the divergence of the vector field at the point p,
// approximated using finite differences with the given step sizes.
func Divergence(p, step Vec, field func(Vec) Vec) float32 {
sx := Vec{X: step.X}
divx := (field(Add(p, sx)).X - field(Sub(p, sx)).X) / step.X
sy := Vec{Y: step.Y}
divy := (field(Add(p, sy)).Y - field(Sub(p, sy)).Y) / step.Y
sz := Vec{Z: step.Z}
divz := (field(Add(p, sz)).Z - field(Sub(p, sz)).Z) / step.Z
return 0.5 * (divx + divy + divz)
}
// Gradient returns the gradient of the scalar field at the point p,
// approximated using finite differences with the given step sizes.
func Gradient(p, step Vec, field func(Vec) float32) Vec {
dx := Vec{X: step.X}
dy := Vec{Y: step.Y}
dz := Vec{Z: step.Z}
return Vec{
X: (field(Add(p, dx)) - field(Sub(p, dx))) / (2 * step.X),
Y: (field(Add(p, dy)) - field(Sub(p, dy))) / (2 * step.Y),
Z: (field(Add(p, dz)) - field(Sub(p, dz))) / (2 * step.Z),
}
}
// MinElem return a vector with the minimum components of two vectors.
func MinElem(a, b Vec) Vec {
return Vec{
X: math.Min(a.X, b.X),
Y: math.Min(a.Y, b.Y),
Z: math.Min(a.Z, b.Z),
}
}
// MaxElem return a vector with the maximum components of two vectors.
func MaxElem(a, b Vec) Vec {
return Vec{
X: math.Max(a.X, b.X),
Y: math.Max(a.Y, b.Y),
Z: math.Max(a.Z, b.Z),
}
}
// AbsElem returns the vector with components set to their absolute value.
func AbsElem(a Vec) Vec {
return Vec{
X: math.Abs(a.X),
Y: math.Abs(a.Y),
Z: math.Abs(a.Z),
}
}
// MulElem returns the Hadamard product between vectors a and b.
//
// v = {a.X*b.X, a.Y*b.Y, a.Z*b.Z}
func MulElem(a, b Vec) Vec {
return Vec{
X: a.X * b.X,
Y: a.Y * b.Y,
Z: a.Z * b.Z,
}
}
// divElem returns the Hadamard product between vector a
// and the inverse components of vector b.
//
// v = {a.X/b.X, a.Y/b.Y, a.Z/b.Z}
func divElem(a, b Vec) Vec {
return Vec{
X: a.X / b.X,
Y: a.Y / b.Y,
Z: a.Z / b.Z,
}
}