staticmap/vendor/github.com/golang/geo/s2/matrix3x3.go

/*
Copyright 2015 Google Inc. All rights reserved.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

package s2

import (
	"fmt"

	"github.com/golang/geo/r3"
)

// matrix3x3 represents a traditional 3x3 matrix of floating point values.
// This is not a full fledged matrix. It only contains the pieces needed
// to satisfy the computations done within the s2 package.
type matrix3x3 [3][3]float64

// col returns the given column as a Point.
func (m *matrix3x3) col(col int) Point {
	return Point{r3.Vector{m[0][col], m[1][col], m[2][col]}}
}

// row returns the given row as a Point.
func (m *matrix3x3) row(row int) Point {
	return Point{r3.Vector{m[row][0], m[row][1], m[row][2]}}
}

// setCol sets the specified column to the value in the given Point.
func (m *matrix3x3) setCol(col int, p Point) *matrix3x3 {
	m[0][col] = p.X
	m[1][col] = p.Y
	m[2][col] = p.Z

	return m
}

// setRow sets the specified row to the value in the given Point.
func (m *matrix3x3) setRow(row int, p Point) *matrix3x3 {
	m[row][0] = p.X
	m[row][1] = p.Y
	m[row][2] = p.Z

	return m
}

// scale multiplies the matrix by the given value.
func (m *matrix3x3) scale(f float64) *matrix3x3 {
	return &matrix3x3{
		[3]float64{f * m[0][0], f * m[0][1], f * m[0][2]},
		[3]float64{f * m[1][0], f * m[1][1], f * m[1][2]},
		[3]float64{f * m[2][0], f * m[2][1], f * m[2][2]},
	}
}

// mul returns the multiplication of m by the Point p and converts the
// resulting 1x3 matrix into a Point.
func (m *matrix3x3) mul(p Point) Point {
	return Point{r3.Vector{
		m[0][0]*p.X + m[0][1]*p.Y + m[0][2]*p.Z,
		m[1][0]*p.X + m[1][1]*p.Y + m[1][2]*p.Z,
		m[2][0]*p.X + m[2][1]*p.Y + m[2][2]*p.Z,
	}}
}

// det returns the determinant of this matrix.
func (m *matrix3x3) det() float64 {
	//      | a  b  c |
	//  det | d  e  f | = aei + bfg + cdh - ceg - bdi - afh
	//      | g  h  i |
	return m[0][0]*m[1][1]*m[2][2] + m[0][1]*m[1][2]*m[2][0] + m[0][2]*m[1][0]*m[2][1] -
		m[0][2]*m[1][1]*m[2][0] - m[0][1]*m[1][0]*m[2][2] - m[0][0]*m[1][2]*m[2][1]
}

// transpose reflects the matrix along its diagonal and returns the result.
func (m *matrix3x3) transpose() *matrix3x3 {
	m[0][1], m[1][0] = m[1][0], m[0][1]
	m[0][2], m[2][0] = m[2][0], m[0][2]
	m[1][2], m[2][1] = m[2][1], m[1][2]

	return m
}

// String formats the matrix into an easier to read layout.
func (m *matrix3x3) String() string {
	return fmt.Sprintf("[ %0.4f %0.4f %0.4f ] [ %0.4f %0.4f %0.4f ] [ %0.4f %0.4f %0.4f ]",
		m[0][0], m[0][1], m[0][2],
		m[1][0], m[1][1], m[1][2],
		m[2][0], m[2][1], m[2][2],
	)
}

// getFrame returns the orthonormal frame for the given point on the unit sphere.
func getFrame(p Point) matrix3x3 {
	// Given the point p on the unit sphere, extend this into a right-handed
	// coordinate frame of unit-length column vectors m = (x,y,z).  Note that
	// the vectors (x,y) are an orthonormal frame for the tangent space at point p,
	// while p itself is an orthonormal frame for the normal space at p.
	m := matrix3x3{}
	m.setCol(2, p)
	m.setCol(1, Point{p.Ortho()})
	m.setCol(0, Point{m.col(1).Cross(p.Vector)})
	return m
}

// toFrame returns the coordinates of the given point with respect to its orthonormal basis m.
// The resulting point q satisfies the identity (m * q == p).
func toFrame(m matrix3x3, p Point) Point {
	// The inverse of an orthonormal matrix is its transpose.
	return m.transpose().mul(p)
}

// fromFrame returns the coordinates of the given point in standard axis-aligned basis
// from its orthonormal basis m.
// The resulting point p satisfies the identity (p == m * q).
func fromFrame(m matrix3x3, q Point) Point {
	return m.mul(q)
}