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

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// 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)
}