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