| // Copyright ©2019 The Gonum 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 r3 |
| |
| import "math" |
| |
| // Vec is a 3D vector. |
| type Vec struct { |
| X, Y, Z float64 |
| } |
| |
| // Add returns the vector sum of p and q. |
| func (p Vec) Add(q Vec) Vec { |
| p.X += q.X |
| p.Y += q.Y |
| p.Z += q.Z |
| return p |
| } |
| |
| // Sub returns the vector sum of p and -q. |
| func (p Vec) Sub(q Vec) Vec { |
| p.X -= q.X |
| p.Y -= q.Y |
| p.Z -= q.Z |
| return p |
| } |
| |
| // Scale returns the vector p scaled by f. |
| func (p Vec) Scale(f float64) Vec { |
| p.X *= f |
| p.Y *= f |
| p.Z *= f |
| return p |
| } |
| |
| // Dot returns the dot product p·q. |
| func (p Vec) Dot(q Vec) float64 { |
| return p.X*q.X + p.Y*q.Y + p.Z*q.Z |
| } |
| |
| // Cross returns the cross product p×q. |
| func (p Vec) Cross(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, |
| } |
| } |
| |
| // Norm returns the Euclidean norm of p |
| // |p| = sqrt(p_x^2 + p_y^2 + p_z^2). |
| func Norm(p Vec) float64 { |
| return math.Hypot(p.X, math.Hypot(p.Y, p.Z)) |
| } |
| |
| // Norm returns the Euclidean squared norm of p |
| // |p|^2 = p_x^2 + p_y^2 + p_z^2. |
| func Norm2(p Vec) float64 { |
| 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 p.Scale(1 / Norm(p)) |
| } |
| |
| // Cos returns the cosine of the opening angle between p and q. |
| func Cos(p, q Vec) float64 { |
| return p.Dot(q) / (Norm(p) * Norm(q)) |
| } |
| |
| // Box is a 3D bounding box. |
| type Box struct { |
| Min, Max Vec |
| } |