mirror of
https://github.com/superseriousbusiness/gotosocial.git
synced 2024-11-26 21:56:39 +00:00
98263a7de6
* start fixing up tests * fix up tests + automate with drone * fiddle with linting * messing about with drone.yml * some more fiddling * hmmm * add cache * add vendor directory * verbose * ci updates * update some little things * update sig
128 lines
4 KiB
Go
128 lines
4 KiB
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)
|
|
}
|