github.com/gopherd/gonum@v0.0.4/spatial/r3/vector.go (about)

     1  // Copyright ©2019 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package r3
     6  
     7  import "math"
     8  
     9  // Vec is a 3D vector.
    10  type Vec struct {
    11  	X, Y, Z float64
    12  }
    13  
    14  // Add returns the vector sum of p and q.
    15  func Add(p, q Vec) Vec {
    16  	return Vec{
    17  		X: p.X + q.X,
    18  		Y: p.Y + q.Y,
    19  		Z: p.Z + q.Z,
    20  	}
    21  }
    22  
    23  // Sub returns the vector sum of p and -q.
    24  func Sub(p, q Vec) Vec {
    25  	return Vec{
    26  		X: p.X - q.X,
    27  		Y: p.Y - q.Y,
    28  		Z: p.Z - q.Z,
    29  	}
    30  }
    31  
    32  // Scale returns the vector p scaled by f.
    33  func Scale(f float64, p Vec) Vec {
    34  	return Vec{
    35  		X: f * p.X,
    36  		Y: f * p.Y,
    37  		Z: f * p.Z,
    38  	}
    39  }
    40  
    41  // Dot returns the dot product p·q.
    42  func Dot(p, q Vec) float64 {
    43  	return p.X*q.X + p.Y*q.Y + p.Z*q.Z
    44  }
    45  
    46  // Cross returns the cross product p×q.
    47  func Cross(p, q Vec) Vec {
    48  	return Vec{
    49  		p.Y*q.Z - p.Z*q.Y,
    50  		p.Z*q.X - p.X*q.Z,
    51  		p.X*q.Y - p.Y*q.X,
    52  	}
    53  }
    54  
    55  // Rotate returns a new vector, rotated by alpha around the provided axis.
    56  func Rotate(p Vec, alpha float64, axis Vec) Vec {
    57  	return NewRotation(alpha, axis).Rotate(p)
    58  }
    59  
    60  // Norm returns the Euclidean norm of p
    61  //  |p| = sqrt(p_x^2 + p_y^2 + p_z^2).
    62  func Norm(p Vec) float64 {
    63  	return math.Hypot(p.X, math.Hypot(p.Y, p.Z))
    64  }
    65  
    66  // Norm2 returns the Euclidean squared norm of p
    67  //  |p|^2 = p_x^2 + p_y^2 + p_z^2.
    68  func Norm2(p Vec) float64 {
    69  	return p.X*p.X + p.Y*p.Y + p.Z*p.Z
    70  }
    71  
    72  // Unit returns the unit vector colinear to p.
    73  // Unit returns {NaN,NaN,NaN} for the zero vector.
    74  func Unit(p Vec) Vec {
    75  	if p.X == 0 && p.Y == 0 && p.Z == 0 {
    76  		return Vec{X: math.NaN(), Y: math.NaN(), Z: math.NaN()}
    77  	}
    78  	return Scale(1/Norm(p), p)
    79  }
    80  
    81  // Cos returns the cosine of the opening angle between p and q.
    82  func Cos(p, q Vec) float64 {
    83  	return Dot(p, q) / (Norm(p) * Norm(q))
    84  }
    85  
    86  // Box is a 3D bounding box.
    87  type Box struct {
    88  	Min, Max Vec
    89  }