fixed dependencies
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nuknal
203
vendor/gonum.org/v1/plot/plotter/conrec.go
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203
vendor/gonum.org/v1/plot/plotter/conrec.go
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// Copyright ©2015 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package plotter
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import (
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"math"
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)
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type point struct {
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X, Y float64
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}
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type line struct {
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p1, p2 point
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}
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func sect(h, p [5]float64, v1, v2 int) float64 {
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return (h[v2]*p[v1] - h[v1]*p[v2]) / (h[v2] - h[v1])
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}
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// conrecLine performs an operation with a line at a given height derived
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// from data over the 2D box interval (i, j) to (i+1, j+1).
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type conrecLine func(i, j int, l line, height float64)
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// conrec is a Go translation of the C version of CONREC by Paul Bourke:
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// http://paulbourke.net/papers/conrec/conrec.c
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//
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// conrec takes g, an m×n grid function, a sorted slice of contour heights
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// and a conrecLine function.
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//
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// For full details of the algorithm, see the paper at
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// http://paulbourke.net/papers/conrec/
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func conrec(g GridXYZ, heights []float64, fn conrecLine) {
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var (
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p1, p2 point
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h [5]float64
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sh [5]int
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xh, yh [5]float64
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im = [4]int{0, 1, 1, 0}
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jm = [4]int{0, 0, 1, 1}
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// We differ from conrec.c in the assignment of a single value
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// in cases (castab in conrec.c). The value of castab[1][1][1] is
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// 3, but we set cases[1][1][1] to 0.
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//
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// axiom: When we have a section of the grid where all the
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// Z values are equal, and equal to a contour height we would
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// expect to have no internal segments to draw.
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//
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// This is covered by case g) in Paul Bourke's description of
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// the CONREC algorithm (a triangle with three vertices the lie
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// on the contour level). He says, "... case g above has no really
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// satisfactory solution and fortunately will occur rarely with
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// real arithmetic." and then goes on to show the following image:
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//
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// http://paulbourke.net/papers/conrec/conrec3.gif
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//
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// which shows case g) in the set where no edge is drawn, agreeing
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// with our axiom above.
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//
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// However, in the iteration over sh at conrec.c +44, a triangle
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// with all vertices on the plane is given sh = {0,0,0,0,0} and
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// then when the switch at conrec.c +93 happens, castab resolves
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// that to case 3 for all values of m.
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//
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// This is fixed by replacing castab/cases[1][1][1] with 0.
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cases = [3][3][3]int{
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{{0, 0, 8}, {0, 2, 5}, {7, 6, 9}},
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{{0, 3, 4}, {1, 0, 1}, {4, 3, 0}},
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{{9, 6, 7}, {5, 2, 0}, {8, 0, 0}},
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}
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)
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c, r := g.Dims()
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for i := 0; i < c-1; i++ {
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for j := 0; j < r-1; j++ {
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dmin := math.Min(
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math.Min(g.Z(i, j), g.Z(i, j+1)),
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math.Min(g.Z(i+1, j), g.Z(i+1, j+1)),
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)
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dmax := math.Max(
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math.Max(g.Z(i, j), g.Z(i, j+1)),
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math.Max(g.Z(i+1, j), g.Z(i+1, j+1)),
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)
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if dmax < heights[0] || heights[len(heights)-1] < dmin {
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continue
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}
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for k := 0; k < len(heights); k++ {
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if heights[k] < dmin || dmax < heights[k] {
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continue
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}
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for m := 4; m >= 0; m-- {
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if m > 0 {
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h[m] = g.Z(i+im[m-1], j+jm[m-1]) - heights[k]
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xh[m] = g.X(i + im[m-1])
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yh[m] = g.Y(j + jm[m-1])
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} else {
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h[0] = 0.25 * (h[1] + h[2] + h[3] + h[4])
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xh[0] = 0.50 * (g.X(i) + g.X(i+1))
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yh[0] = 0.50 * (g.Y(j) + g.Y(j+1))
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}
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switch {
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case h[m] > 0:
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sh[m] = 1
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case h[m] < 0:
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sh[m] = -1
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default:
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sh[m] = 0
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}
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}
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/*
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Note: at this stage the relative heights of the corners and the
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centre are in the h array, and the corresponding coordinates are
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in the xh and yh arrays. The centre of the box is indexed by 0
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and the 4 corners by 1 to 4 as shown below.
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Each triangle is then indexed by the parameter m, and the 3
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vertices of each triangle are indexed by parameters m1,m2,and m3.
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It is assumed that the centre of the box is always vertex 2
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though this isimportant only when all 3 vertices lie exactly on
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the same contour level, in which case only the side of the box
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is drawn.
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vertex 4 +-------------------+ vertex 3
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| \ / |
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| \ m-3 / |
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| \ / |
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| \ / |
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| m=2 X m=2 | the centre is vertex 0
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| / \ |
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| / \ |
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| / m=1 \ |
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| / \ |
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vertex 1 +-------------------+ vertex 2
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*/
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// Scan each triangle in the box.
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for m := 1; m <= 4; m++ {
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m1 := m
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const m2 = 0
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var m3 int
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if m != 4 {
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m3 = m + 1
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} else {
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m3 = 1
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}
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switch cases[sh[m1]+1][sh[m2]+1][sh[m3]+1] {
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case 0:
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continue
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case 1: // Line between vertices 1 and 2
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p1 = point{X: xh[m1], Y: yh[m1]}
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p2 = point{X: xh[m2], Y: yh[m2]}
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case 2: // Line between vertices 2 and 3
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p1 = point{X: xh[m2], Y: yh[m2]}
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p2 = point{X: xh[m3], Y: yh[m3]}
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case 3: // Line between vertices 3 and 1
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p1 = point{X: xh[m3], Y: yh[m3]}
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p2 = point{X: xh[m1], Y: yh[m1]}
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case 4: // Line between vertex 1 and side 2-3
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p1 = point{X: xh[m1], Y: yh[m1]}
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p2 = point{X: sect(h, xh, m2, m3), Y: sect(h, yh, m2, m3)}
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case 5: // Line between vertex 2 and side 3-1
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p1 = point{X: xh[m2], Y: yh[m2]}
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p2 = point{X: sect(h, xh, m3, m1), Y: sect(h, yh, m3, m1)}
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case 6: // Line between vertex 3 and side 1-2
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p1 = point{X: xh[m3], Y: yh[m3]}
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p2 = point{X: sect(h, xh, m1, m2), Y: sect(h, yh, m1, m2)}
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case 7: // Line between sides 1-2 and 2-3
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p1 = point{X: sect(h, xh, m1, m2), Y: sect(h, yh, m1, m2)}
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p2 = point{X: sect(h, xh, m2, m3), Y: sect(h, yh, m2, m3)}
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case 8: // Line between sides 2-3 and 3-1
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p1 = point{X: sect(h, xh, m2, m3), Y: sect(h, yh, m2, m3)}
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p2 = point{X: sect(h, xh, m3, m1), Y: sect(h, yh, m3, m1)}
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case 9: // Line between sides 3-1 and 1-2
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p1 = point{X: sect(h, xh, m3, m1), Y: sect(h, yh, m3, m1)}
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p2 = point{X: sect(h, xh, m1, m2), Y: sect(h, yh, m1, m2)}
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default:
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panic("cannot reach")
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}
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fn(i, j, line{p1: p1, p2: p2}, heights[k])
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}
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}
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}
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}
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}
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