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90 lines
1.8 KiB
Go
90 lines
1.8 KiB
Go
// Copyright ©2019 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package r3
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import "math"
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// Vec is a 3D vector.
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type Vec struct {
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X, Y, Z float64
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}
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// Add returns the vector sum of p and q.
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func Add(p, q Vec) Vec {
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return Vec{
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X: p.X + q.X,
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Y: p.Y + q.Y,
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Z: p.Z + q.Z,
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}
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}
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// Sub returns the vector sum of p and -q.
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func Sub(p, q Vec) Vec {
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return Vec{
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X: p.X - q.X,
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Y: p.Y - q.Y,
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Z: p.Z - q.Z,
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}
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}
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// Scale returns the vector p scaled by f.
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func Scale(f float64, p Vec) Vec {
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return Vec{
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X: f * p.X,
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Y: f * p.Y,
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Z: f * p.Z,
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}
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}
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// Dot returns the dot product p·q.
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func Dot(p, q Vec) float64 {
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return p.X*q.X + p.Y*q.Y + p.Z*q.Z
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}
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// Cross returns the cross product p×q.
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func Cross(p, q Vec) Vec {
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return Vec{
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p.Y*q.Z - p.Z*q.Y,
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p.Z*q.X - p.X*q.Z,
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p.X*q.Y - p.Y*q.X,
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}
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}
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// Rotate returns a new vector, rotated by alpha around the provided axis.
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func Rotate(p Vec, alpha float64, axis Vec) Vec {
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return NewRotation(alpha, axis).Rotate(p)
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}
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// Norm returns the Euclidean norm of p
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// |p| = sqrt(p_x^2 + p_y^2 + p_z^2).
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func Norm(p Vec) float64 {
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return math.Hypot(p.X, math.Hypot(p.Y, p.Z))
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}
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// Norm2 returns the Euclidean squared norm of p
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// |p|^2 = p_x^2 + p_y^2 + p_z^2.
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func Norm2(p Vec) float64 {
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return p.X*p.X + p.Y*p.Y + p.Z*p.Z
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}
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// Unit returns the unit vector colinear to p.
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// Unit returns {NaN,NaN,NaN} for the zero vector.
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func Unit(p Vec) Vec {
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if p.X == 0 && p.Y == 0 && p.Z == 0 {
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return Vec{X: math.NaN(), Y: math.NaN(), Z: math.NaN()}
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}
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return Scale(1/Norm(p), p)
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}
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// Cos returns the cosine of the opening angle between p and q.
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func Cos(p, q Vec) float64 {
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return Dot(p, q) / (Norm(p) * Norm(q))
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}
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// Box is a 3D bounding box.
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type Box struct {
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Min, Max Vec
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}
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