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Diffstat (limited to 'vendor/github.com/golang/geo/s2/matrix3x3.go')
| -rw-r--r-- | vendor/github.com/golang/geo/s2/matrix3x3.go | 127 |
1 files changed, 127 insertions, 0 deletions
diff --git a/vendor/github.com/golang/geo/s2/matrix3x3.go b/vendor/github.com/golang/geo/s2/matrix3x3.go new file mode 100644 index 000000000..01696fe83 --- /dev/null +++ b/vendor/github.com/golang/geo/s2/matrix3x3.go @@ -0,0 +1,127 @@ +// 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) +} |