128 lines
4.0 KiB
Go
128 lines
4.0 KiB
Go
// Copyright 2015 Google Inc. All rights reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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package s2
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import (
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"fmt"
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"github.com/golang/geo/r3"
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)
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// matrix3x3 represents a traditional 3x3 matrix of floating point values.
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// This is not a full fledged matrix. It only contains the pieces needed
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// to satisfy the computations done within the s2 package.
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type matrix3x3 [3][3]float64
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// col returns the given column as a Point.
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func (m *matrix3x3) col(col int) Point {
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return Point{r3.Vector{m[0][col], m[1][col], m[2][col]}}
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}
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// row returns the given row as a Point.
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func (m *matrix3x3) row(row int) Point {
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return Point{r3.Vector{m[row][0], m[row][1], m[row][2]}}
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}
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// setCol sets the specified column to the value in the given Point.
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func (m *matrix3x3) setCol(col int, p Point) *matrix3x3 {
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m[0][col] = p.X
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m[1][col] = p.Y
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m[2][col] = p.Z
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return m
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}
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// setRow sets the specified row to the value in the given Point.
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func (m *matrix3x3) setRow(row int, p Point) *matrix3x3 {
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m[row][0] = p.X
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m[row][1] = p.Y
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m[row][2] = p.Z
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return m
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}
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// scale multiplies the matrix by the given value.
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func (m *matrix3x3) scale(f float64) *matrix3x3 {
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return &matrix3x3{
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[3]float64{f * m[0][0], f * m[0][1], f * m[0][2]},
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[3]float64{f * m[1][0], f * m[1][1], f * m[1][2]},
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[3]float64{f * m[2][0], f * m[2][1], f * m[2][2]},
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}
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}
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// mul returns the multiplication of m by the Point p and converts the
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// resulting 1x3 matrix into a Point.
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func (m *matrix3x3) mul(p Point) Point {
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return Point{r3.Vector{
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m[0][0]*p.X + m[0][1]*p.Y + m[0][2]*p.Z,
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m[1][0]*p.X + m[1][1]*p.Y + m[1][2]*p.Z,
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m[2][0]*p.X + m[2][1]*p.Y + m[2][2]*p.Z,
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}}
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}
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// det returns the determinant of this matrix.
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func (m *matrix3x3) det() float64 {
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// | a b c |
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// det | d e f | = aei + bfg + cdh - ceg - bdi - afh
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// | g h i |
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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] -
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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]
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}
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// transpose reflects the matrix along its diagonal and returns the result.
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func (m *matrix3x3) transpose() *matrix3x3 {
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m[0][1], m[1][0] = m[1][0], m[0][1]
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m[0][2], m[2][0] = m[2][0], m[0][2]
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m[1][2], m[2][1] = m[2][1], m[1][2]
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return m
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}
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// String formats the matrix into an easier to read layout.
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func (m *matrix3x3) String() string {
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return fmt.Sprintf("[ %0.4f %0.4f %0.4f ] [ %0.4f %0.4f %0.4f ] [ %0.4f %0.4f %0.4f ]",
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m[0][0], m[0][1], m[0][2],
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m[1][0], m[1][1], m[1][2],
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m[2][0], m[2][1], m[2][2],
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)
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}
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// getFrame returns the orthonormal frame for the given point on the unit sphere.
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func getFrame(p Point) matrix3x3 {
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// Given the point p on the unit sphere, extend this into a right-handed
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// coordinate frame of unit-length column vectors m = (x,y,z). Note that
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// the vectors (x,y) are an orthonormal frame for the tangent space at point p,
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// while p itself is an orthonormal frame for the normal space at p.
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m := matrix3x3{}
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m.setCol(2, p)
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m.setCol(1, Point{p.Ortho()})
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m.setCol(0, Point{m.col(1).Cross(p.Vector)})
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return m
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}
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// toFrame returns the coordinates of the given point with respect to its orthonormal basis m.
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// The resulting point q satisfies the identity (m * q == p).
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func toFrame(m matrix3x3, p Point) Point {
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// The inverse of an orthonormal matrix is its transpose.
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return m.transpose().mul(p)
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}
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// fromFrame returns the coordinates of the given point in standard axis-aligned basis
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// from its orthonormal basis m.
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// The resulting point p satisfies the identity (p == m * q).
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func fromFrame(m matrix3x3, q Point) Point {
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return m.mul(q)
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}
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