mirror of
https://github.com/Luzifer/staticmap.git
synced 2025-01-02 03:01:17 +00:00
305 lines
8.5 KiB
Go
305 lines
8.5 KiB
Go
/*
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Copyright 2014 Google Inc. All rights reserved.
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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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http://www.apache.org/licenses/LICENSE-2.0
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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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*/
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package s2
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import (
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"math"
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"github.com/golang/geo/r3"
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)
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const (
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// maxSiTi is the maximum value of an si- or ti-coordinate.
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// It is one shift more than maxSize.
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maxSiTi = maxSize << 1
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)
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// siTiToST converts an si- or ti-value to the corresponding s- or t-value.
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// Value is capped at 1.0 because there is no DCHECK in Go.
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func siTiToST(si uint64) float64 {
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if si > maxSiTi {
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return 1.0
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}
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return float64(si) / float64(maxSiTi)
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}
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// stToSiTi converts the s- or t-value to the nearest si- or ti-coordinate.
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// The result may be outside the range of valid (si,ti)-values. Value of
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// 0.49999999999999994 (math.NextAfter(0.5, -1)), will be incorrectly rounded up.
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func stToSiTi(s float64) uint64 {
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if s < 0 {
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return uint64(s*maxSiTi - 0.5)
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}
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return uint64(s*maxSiTi + 0.5)
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}
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// stToUV converts an s or t value to the corresponding u or v value.
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// This is a non-linear transformation from [-1,1] to [-1,1] that
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// attempts to make the cell sizes more uniform.
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// This uses what the C++ version calls 'the quadratic transform'.
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func stToUV(s float64) float64 {
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if s >= 0.5 {
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return (1 / 3.) * (4*s*s - 1)
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}
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return (1 / 3.) * (1 - 4*(1-s)*(1-s))
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}
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// uvToST is the inverse of the stToUV transformation. Note that it
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// is not always true that uvToST(stToUV(x)) == x due to numerical
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// errors.
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func uvToST(u float64) float64 {
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if u >= 0 {
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return 0.5 * math.Sqrt(1+3*u)
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}
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return 1 - 0.5*math.Sqrt(1-3*u)
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}
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// face returns face ID from 0 to 5 containing the r. For points on the
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// boundary between faces, the result is arbitrary but deterministic.
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func face(r r3.Vector) int {
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f := r.LargestComponent()
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switch {
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case f == r3.XAxis && r.X < 0:
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f += 3
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case f == r3.YAxis && r.Y < 0:
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f += 3
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case f == r3.ZAxis && r.Z < 0:
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f += 3
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}
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return int(f)
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}
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// validFaceXYZToUV given a valid face for the given point r (meaning that
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// dot product of r with the face normal is positive), returns
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// the corresponding u and v values, which may lie outside the range [-1,1].
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func validFaceXYZToUV(face int, r r3.Vector) (float64, float64) {
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switch face {
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case 0:
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return r.Y / r.X, r.Z / r.X
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case 1:
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return -r.X / r.Y, r.Z / r.Y
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case 2:
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return -r.X / r.Z, -r.Y / r.Z
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case 3:
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return r.Z / r.X, r.Y / r.X
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case 4:
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return r.Z / r.Y, -r.X / r.Y
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}
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return -r.Y / r.Z, -r.X / r.Z
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}
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// xyzToFaceUV converts a direction vector (not necessarily unit length) to
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// (face, u, v) coordinates.
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func xyzToFaceUV(r r3.Vector) (f int, u, v float64) {
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f = face(r)
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u, v = validFaceXYZToUV(f, r)
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return f, u, v
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}
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// faceUVToXYZ turns face and UV coordinates into an unnormalized 3 vector.
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func faceUVToXYZ(face int, u, v float64) r3.Vector {
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switch face {
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case 0:
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return r3.Vector{1, u, v}
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case 1:
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return r3.Vector{-u, 1, v}
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case 2:
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return r3.Vector{-u, -v, 1}
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case 3:
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return r3.Vector{-1, -v, -u}
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case 4:
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return r3.Vector{v, -1, -u}
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default:
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return r3.Vector{v, u, -1}
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}
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}
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// faceXYZToUV returns the u and v values (which may lie outside the range
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// [-1, 1]) if the dot product of the point p with the given face normal is positive.
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func faceXYZToUV(face int, p Point) (u, v float64, ok bool) {
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switch face {
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case 0:
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if p.X <= 0 {
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return 0, 0, false
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}
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case 1:
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if p.Y <= 0 {
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return 0, 0, false
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}
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case 2:
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if p.Z <= 0 {
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return 0, 0, false
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}
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case 3:
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if p.X >= 0 {
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return 0, 0, false
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}
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case 4:
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if p.Y >= 0 {
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return 0, 0, false
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}
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default:
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if p.Z >= 0 {
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return 0, 0, false
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}
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}
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u, v = validFaceXYZToUV(face, p.Vector)
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return u, v, true
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}
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// faceXYZtoUVW transforms the given point P to the (u,v,w) coordinate frame of the given
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// face where the w-axis represents the face normal.
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func faceXYZtoUVW(face int, p Point) Point {
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// The result coordinates are simply the dot products of P with the (u,v,w)
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// axes for the given face (see faceUVWAxes).
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switch face {
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case 0:
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return Point{r3.Vector{p.Y, p.Z, p.X}}
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case 1:
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return Point{r3.Vector{-p.X, p.Z, p.Y}}
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case 2:
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return Point{r3.Vector{-p.X, -p.Y, p.Z}}
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case 3:
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return Point{r3.Vector{-p.Z, -p.Y, -p.X}}
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case 4:
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return Point{r3.Vector{-p.Z, p.X, -p.Y}}
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default:
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return Point{r3.Vector{p.Y, p.X, -p.Z}}
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}
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}
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// faceSiTiToXYZ transforms the (si, ti) coordinates to a (not necessarily
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// unit length) Point on the given face.
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func faceSiTiToXYZ(face int, si, ti uint64) Point {
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return Point{faceUVToXYZ(face, stToUV(siTiToST(si)), stToUV(siTiToST(ti)))}
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}
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// xyzToFaceSiTi transforms the (not necessarily unit length) Point to
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// (face, si, ti) coordinates and the level the Point is at.
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func xyzToFaceSiTi(p Point) (face int, si, ti uint64, level int) {
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face, u, v := xyzToFaceUV(p.Vector)
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si = stToSiTi(uvToST(u))
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ti = stToSiTi(uvToST(v))
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// If the levels corresponding to si,ti are not equal, then p is not a cell
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// center. The si,ti values of 0 and maxSiTi need to be handled specially
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// because they do not correspond to cell centers at any valid level; they
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// are mapped to level -1 by the code at the end.
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level = maxLevel - findLSBSetNonZero64(si|maxSiTi)
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if level < 0 || level != maxLevel-findLSBSetNonZero64(ti|maxSiTi) {
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return face, si, ti, -1
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}
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// In infinite precision, this test could be changed to ST == SiTi. However,
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// due to rounding errors, uvToST(xyzToFaceUV(faceUVToXYZ(stToUV(...)))) is
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// not idempotent. On the other hand, the center is computed exactly the same
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// way p was originally computed (if it is indeed the center of a Cell);
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// the comparison can be exact.
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if p.Vector == faceSiTiToXYZ(face, si, ti).Normalize() {
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return face, si, ti, level
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}
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return face, si, ti, -1
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}
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// uNorm returns the right-handed normal (not necessarily unit length) for an
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// edge in the direction of the positive v-axis at the given u-value on
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// the given face. (This vector is perpendicular to the plane through
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// the sphere origin that contains the given edge.)
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func uNorm(face int, u float64) r3.Vector {
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switch face {
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case 0:
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return r3.Vector{u, -1, 0}
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case 1:
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return r3.Vector{1, u, 0}
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case 2:
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return r3.Vector{1, 0, u}
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case 3:
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return r3.Vector{-u, 0, 1}
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case 4:
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return r3.Vector{0, -u, 1}
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default:
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return r3.Vector{0, -1, -u}
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}
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}
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// vNorm returns the right-handed normal (not necessarily unit length) for an
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// edge in the direction of the positive u-axis at the given v-value on
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// the given face.
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func vNorm(face int, v float64) r3.Vector {
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switch face {
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case 0:
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return r3.Vector{-v, 0, 1}
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case 1:
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return r3.Vector{0, -v, 1}
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case 2:
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return r3.Vector{0, -1, -v}
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case 3:
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return r3.Vector{v, -1, 0}
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case 4:
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return r3.Vector{1, v, 0}
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default:
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return r3.Vector{1, 0, v}
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}
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}
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// faceUVWAxes are the U, V, and W axes for each face.
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var faceUVWAxes = [6][3]Point{
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{Point{r3.Vector{0, 1, 0}}, Point{r3.Vector{0, 0, 1}}, Point{r3.Vector{1, 0, 0}}},
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{Point{r3.Vector{-1, 0, 0}}, Point{r3.Vector{0, 0, 1}}, Point{r3.Vector{0, 1, 0}}},
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{Point{r3.Vector{-1, 0, 0}}, Point{r3.Vector{0, -1, 0}}, Point{r3.Vector{0, 0, 1}}},
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{Point{r3.Vector{0, 0, -1}}, Point{r3.Vector{0, -1, 0}}, Point{r3.Vector{-1, 0, 0}}},
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{Point{r3.Vector{0, 0, -1}}, Point{r3.Vector{1, 0, 0}}, Point{r3.Vector{0, -1, 0}}},
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{Point{r3.Vector{0, 1, 0}}, Point{r3.Vector{1, 0, 0}}, Point{r3.Vector{0, 0, -1}}},
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}
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// faceUVWFaces are the precomputed neighbors of each face.
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var faceUVWFaces = [6][3][2]int{
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{{4, 1}, {5, 2}, {3, 0}},
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{{0, 3}, {5, 2}, {4, 1}},
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{{0, 3}, {1, 4}, {5, 2}},
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{{2, 5}, {1, 4}, {0, 3}},
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{{2, 5}, {3, 0}, {1, 4}},
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{{4, 1}, {3, 0}, {2, 5}},
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}
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// uvwAxis returns the given axis of the given face.
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func uvwAxis(face, axis int) Point {
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return faceUVWAxes[face][axis]
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}
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// uvwFaces returns the face in the (u,v,w) coordinate system on the given axis
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// in the given direction.
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func uvwFace(face, axis, direction int) int {
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return faceUVWFaces[face][axis][direction]
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}
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// uAxis returns the u-axis for the given face.
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func uAxis(face int) Point {
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return uvwAxis(face, 0)
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}
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// vAxis returns the v-axis for the given face.
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func vAxis(face int) Point {
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return uvwAxis(face, 1)
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}
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// Return the unit-length normal for the given face.
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func unitNorm(face int) Point {
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return uvwAxis(face, 2)
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}
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