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 // 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 r2 import "math" // Vec is a 2D vector. type Vec struct { X, Y 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 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 return p } // Scale returns the vector p scaled by f. func (p Vec) Scale(f float64) Vec { p.X *= f p.Y *= 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 } // Cross returns the cross product p×q. func (p Vec) Cross(q Vec) float64 { return p.X*q.Y - p.Y*q.X } // Rotate returns a new vector, rotated by alpha around the provided point, q. func (p Vec) Rotate(alpha float64, q Vec) Vec { return NewRotation(alpha, q).Rotate(p) } // Norm returns the Euclidean norm of p // |p| = sqrt(p_x^2 + p_y^2). func Norm(p Vec) float64 { return math.Hypot(p.X, p.Y) } // Norm returns the Euclidean squared norm of p // |p|^2 = p_x^2 + p_y^2. func Norm2(p Vec) float64 { return p.X*p.X + p.Y*p.Y } // Unit returns the unit vector colinear to p. // Unit returns {NaN,NaN} for the zero vector. func Unit(p Vec) Vec { if p.X == 0 && p.Y == 0 { return Vec{X: math.NaN(), Y: 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 2D bounding box. type Box struct { Min, Max Vec } // Rotation describes a rotation in 2D. type Rotation struct { sin, cos float64 p Vec } // NewRotation creates a rotation by alpha, around p. func NewRotation(alpha float64, p Vec) Rotation { if alpha == 0 { return Rotation{sin: 0, cos: 1, p: p} } sin, cos := math.Sincos(alpha) return Rotation{sin: sin, cos: cos, p: p} } // Rotate returns the rotated vector according to the definition of rot. func (r Rotation) Rotate(p Vec) Vec { if r.isIdentity() { return p } o := p.Sub(r.p) return Vec{ X: (o.X*r.cos - o.Y*r.sin), Y: (o.X*r.sin + o.Y*r.cos), }.Add(r.p) } func (r Rotation) isIdentity() bool { return r.sin == 0 && r.cos == 1 }