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path_test.go
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package canvas
import (
"fmt"
"math"
"os"
"strings"
"testing"
"github.com/tdewolff/test"
"gonum.org/v1/plot"
"gonum.org/v1/plot/plotter"
"gonum.org/v1/plot/vg"
"gonum.org/v1/plot/vg/draw"
)
func TestPathEmpty(t *testing.T) {
p := &Path{}
test.That(t, p.Empty())
p.MoveTo(5, 2)
test.That(t, p.Empty())
p.LineTo(6, 2)
test.That(t, !p.Empty())
}
func TestPathEquals(t *testing.T) {
test.That(t, !MustParseSVGPath("M5 0L5 10").Equals(MustParseSVGPath("M5 0")))
test.That(t, !MustParseSVGPath("M5 0L5 10").Equals(MustParseSVGPath("M5 0M5 10")))
test.That(t, !MustParseSVGPath("M5 0L5 10").Equals(MustParseSVGPath("M5 0L5 9")))
test.That(t, MustParseSVGPath("M5 0L5 10").Equals(MustParseSVGPath("M5 0L5 10")))
}
func TestPathSame(t *testing.T) {
test.That(t, MustParseSVGPath("L1 0L1 1L0 1z").Same(MustParseSVGPath("L0 1L1 1L1 0z")))
}
func TestPathClosed(t *testing.T) {
test.That(t, !MustParseSVGPath("M5 0L5 10").Closed())
test.That(t, MustParseSVGPath("M5 0L5 10z").Closed())
test.That(t, !MustParseSVGPath("M5 0L5 10zM5 10").Closed())
test.That(t, MustParseSVGPath("M5 0L5 10zM5 10z").Closed())
}
func TestPathAppend(t *testing.T) {
test.T(t, MustParseSVGPath("M5 0L5 10").Append(nil), MustParseSVGPath("M5 0L5 10"))
test.T(t, (&Path{}).Append(MustParseSVGPath("M5 0L5 10")), MustParseSVGPath("M5 0L5 10"))
p := MustParseSVGPath("M5 0L5 10").Append(MustParseSVGPath("M5 15L10 15"))
test.T(t, p, MustParseSVGPath("M5 0L5 10M5 15L10 15"))
p = MustParseSVGPath("M5 0L5 10").Append(MustParseSVGPath("L10 15M20 15L25 15"))
test.T(t, p, MustParseSVGPath("M5 0L5 10M0 0L10 15M20 15L25 15"))
}
func TestPathJoin(t *testing.T) {
var tests = []struct {
p, q string
expected string
}{
{"M5 0L5 10", "", "M5 0L5 10"},
{"", "M5 0L5 10", "M5 0L5 10"},
{"M5 0L5 10", "L10 15", "M5 0L5 10M0 0L10 15"},
{"M5 0L5 10z", "M5 0L10 15", "M5 0L5 10zM5 0L10 15"},
{"M5 0L5 10", "M5 10L10 15", "M5 0L5 10L10 15"},
{"M5 0L5 10", "L10 15M20 15L25 15", "M5 0L5 10M0 0L10 15M20 15L25 15"},
{"M5 0L5 10", "M5 10L10 15M20 15L25 15", "M5 0L5 10L10 15M20 15L25 15"},
{"M5 0L10 5", "M10 5L15 10", "M5 0L15 10"},
{"M5 0L10 5", "L5 5z", "M5 0L10 5M0 0L5 5z"},
}
for _, tt := range tests {
t.Run(fmt.Sprint(tt.p, "x", tt.q), func(t *testing.T) {
p := MustParseSVGPath(tt.p).Join(MustParseSVGPath(tt.q))
test.T(t, p, MustParseSVGPath(tt.expected))
})
}
test.T(t, MustParseSVGPath("M5 0L5 10").Join(nil), MustParseSVGPath("M5 0L5 10"))
}
func TestPathCoords(t *testing.T) {
coords := MustParseSVGPath("L5 10").Coords()
test.T(t, len(coords), 2)
test.T(t, coords[0], Point{0.0, 0.0})
test.T(t, coords[1], Point{5.0, 10.0})
coords = MustParseSVGPath("L5 10C2.5 10 0 5 0 0z").Coords()
test.T(t, len(coords), 3)
test.T(t, coords[0], Point{0.0, 0.0})
test.T(t, coords[1], Point{5.0, 10.0})
test.T(t, coords[2], Point{0.0, 0.0})
}
func TestPathCommands(t *testing.T) {
var tts = []struct {
p string
expected string
}{
{"M3 4", "M3 4"},
{"M3 4M5 3", "M5 3"},
{"M3 4z", ""},
{"z", ""},
{"L3 4", "L3 4"},
{"L3 4L0 0z", "L3 4z"},
{"L3 4L4 0L2 0z", "L3 4L4 0z"},
{"L3 4zz", "L3 4z"},
{"L5 0zL6 3", "L5 0zL6 3"},
{"M2 1L3 4L5 0zL6 3", "M2 1L3 4L5 0zM2 1L6 3"},
{"M2 1L3 4L5 0zM2 1L6 3", "M2 1L3 4L5 0zM2 1L6 3"},
{"M3 4Q3 4 3 4", "M3 4"},
{"Q0 0 0 0", ""},
{"Q3 4 3 4", "L3 4"},
{"Q1.5 2 3 4", "L3 4"},
{"Q0 0 -1 -1", "L-1 -1"},
{"Q1 2 3 4", "Q1 2 3 4"},
{"Q3 4 0 0", "Q3 4 0 0"},
{"L5 0zQ5 3 6 3", "L5 0zQ5 3 6 3"},
{"M3 4C3 4 3 4 3 4", "M3 4"},
{"C0 0 0 0 0 0", ""},
{"C0 0 3 4 3 4", "L3 4"},
{"C1 1 2 2 3 3", "L3 3"},
{"C0 0 0 0 -1 -1", "L-1 -1"},
{"C-1 -1 0 0 -1 -1", "L-1 -1"},
{"C1 1 2 2 3 3", "L3 3"},
{"C1 1 2 2 3 4", "C1 1 2 2 3 4"},
{"C1 1 2 2 0 0", "C1 1 2 2 0 0"},
{"C3 3 -1 -1 2 2", "C3 3 -1 -1 2 2"},
{"L5 0zC5 1 5 3 6 3", "L5 0zC5 1 5 3 6 3"},
{"M3 4A2 2 0 0 0 3 4", "M3 4"},
{"A0 0 0 0 0 4 0", "L4 0"},
{"A2 1 0 0 0 4 0", "A2 1 0 0 0 4 0"},
{"A1 2 0 1 1 4 0", "A4 2 90 1 1 4 0"},
{"A1 2 90 0 0 4 0", "A2 1 0 0 0 4 0"},
{"L5 0zA5 5 0 0 0 10 0", "L5 0zA5 5 0 0 0 10 0"},
}
for _, tt := range tts {
t.Run(fmt.Sprint(tt.p), func(t *testing.T) {
test.T(t, MustParseSVGPath(tt.p), MustParseSVGPath(tt.expected))
})
}
p := &Path{}
p.Arc(2, 1, 0, 180, 0)
test.T(t, p, MustParseSVGPath("A2 1 0 0 0 4 0"))
p = &Path{}
p.Arc(2, 1, 0, 0, 180)
test.T(t, p, MustParseSVGPath("A2 1 0 0 1 -4 0"))
p = &Path{}
p.Arc(2, 1, 0, 540, 0)
test.T(t, p, MustParseSVGPath("A2 1 0 0 0 4 0A2 1 0 0 0 0 0A2 1 0 0 0 4 0"))
p = &Path{}
p.Arc(2, 1, 0, 180, -180)
test.T(t, p, MustParseSVGPath("A2 1 0 0 0 4 0A2 1 0 0 0 0 0"))
}
func TestPathCrossingsWindings(t *testing.T) {
var tts = []struct {
p string
pos Point
crossings int
windings int
boundary bool
}{
// within bbox of segment
{"L10 10", Point{2.0, 5.0}, 1, 1, false},
{"L-10 10", Point{-2.0, 5.0}, 0, 0, false},
{"Q10 5 0 10", Point{2.0, 5.0}, 1, 1, false},
{"Q-10 5 0 10", Point{-2.0, 5.0}, 0, 0, false},
{"C10 0 10 10 0 10", Point{2.0, 5.0}, 1, 1, false},
{"C-10 0 -10 10 0 10", Point{-2.0, 5.0}, 0, 0, false},
{"A5 5 0 0 1 0 10", Point{2.0, 5.0}, 1, 1, false},
{"A5 5 0 0 0 0 10", Point{-2.0, 5.0}, 0, 0, false},
{"L10 0L10 10L0 10z", Point{5.0, 5.0}, 1, 1, false}, // mid
{"L0 10L10 10L10 0z", Point{5.0, 5.0}, 1, -1, false}, // mid
// on boundary
{"L10 0L10 10L0 10z", Point{0.0, 5.0}, 1, 0, true}, // left
{"L10 0L10 10L0 10z", Point{10.0, 5.0}, 0, 0, true}, // right
{"L10 0L10 10L0 10z", Point{0.0, 0.0}, 0, 0, true}, // bottom-left
{"L10 0L10 10L0 10z", Point{5.0, 0.0}, 0, 0, true}, // bottom
{"L10 0L10 10L0 10z", Point{10.0, 0.0}, 0, 0, true}, // bottom-right
{"L10 0L10 10L0 10z", Point{0.0, 10.0}, 0, 0, true}, // top-left
{"L10 0L10 10L0 10z", Point{5.0, 10.0}, 0, 0, true}, // top
{"L10 0L10 10L0 10z", Point{10.0, 10.0}, 0, 0, true}, // top-right
{"L0 10L10 10L10 0z", Point{0.0, 5.0}, 1, 0, true}, // left
{"L0 10L10 10L10 0z", Point{10.0, 5.0}, 0, 0, true}, // right
{"L0 10L10 10L10 0z", Point{0.0, 0.0}, 0, 0, true}, // bottom-left
{"L0 10L10 10L10 0z", Point{5.0, 0.0}, 0, 0, true}, // bottom
{"L0 10L10 10L10 0z", Point{10.0, 0.0}, 0, 0, true}, // bottom-right
{"L0 10L10 10L10 0z", Point{0.0, 10.0}, 0, 0, true}, // top-left
{"L0 10L10 10L10 0z", Point{5.0, 10.0}, 0, 0, true}, // top
{"L0 10L10 10L10 0z", Point{10.0, 10.0}, 0, 0, true}, // top-right
// outside
{"L10 0L10 10L0 10z", Point{-1.0, 0.0}, 0, 0, false}, // bottom-left
{"L10 0L10 10L0 10z", Point{-1.0, 5.0}, 2, 0, false}, // left
{"L10 0L10 10L0 10z", Point{-1.0, 10.0}, 0, 0, false}, // top-left
{"L10 0L10 10L0 10z", Point{11.0, 0.0}, 0, 0, false}, // bottom-right
{"L10 0L10 10L0 10z", Point{11.0, 5.0}, 0, 0, false}, // right
{"L10 0L10 10L0 10z", Point{11.0, 10.0}, 0, 0, false}, // top-right
{"L0 10L10 10L10 0z", Point{-1.0, 0.0}, 0, 0, false}, // bottom-left
{"L0 10L10 10L10 0z", Point{-1.0, 5.0}, 2, 0, false}, // left
{"L0 10L10 10L10 0z", Point{-1.0, 10.0}, 0, 0, false}, // top-left
{"L0 10L10 10L10 0z", Point{11.0, 0.0}, 0, 0, false}, // bottom-right
{"L0 10L10 10L10 0z", Point{11.0, 5.0}, 0, 0, false}, // right
{"L0 10L10 10L10 0z", Point{11.0, 10.0}, 0, 0, false}, // top-right
{"L10 0L10 10L0 10L1 5z", Point{0.0, 5.0}, 2, 0, false}, // left over endpoints
// subpath
{"L10 0L10 10L0 10zM2 2L8 2L8 8L2 8z", Point{1.0, 1.0}, 1, 1, false},
{"L10 0L10 10L0 10zM2 2L8 2L8 8L2 8z", Point{3.0, 3.0}, 2, 2, false},
{"L10 0L10 10L0 10zM2 2L2 8L8 8L8 2z", Point{3.0, 3.0}, 2, 0, false},
{"L10 0L10 10L0 10zM2 2L2 8L8 8L8 2z", Point{0.0, 0.0}, 0, 0, true},
{"L10 0L10 10L0 10zM2 2L2 8L8 8L8 2z", Point{2.0, 2.0}, 1, 1, true},
{"L10 0L10 10L0 10zM2 2L8 2L8 8L2 8z", Point{2.0, 2.0}, 1, 1, true},
{"L10 0L10 10L0 10zM5 5L15 5L15 15L5 15z", Point{7.5, 5.0}, 1, 1, true},
// on segment end
{"L5 -5L10 0L5 5z", Point{5.0, 0.0}, 1, 1, false}, // mid
{"L5 -5L10 0L5 5z", Point{0.0, 0.0}, 1, 0, true}, // left
{"L5 -5L10 0L5 5z", Point{10.0, 0.0}, 0, 0, true}, // right
{"L5 -5L10 0L5 5z", Point{5.0, 5.0}, 0, 0, true}, // top
{"L5 -5L10 0L5 5z", Point{5.0, -5.0}, 0, 0, true}, // bottom
{"L5 5L10 0L5 -5z", Point{5.0, 0.0}, 1, -1, false}, // mid
{"L5 5L10 0L5 -5z", Point{0.0, 0.0}, 1, 0, true}, // left
{"L5 5L10 0L5 -5z", Point{10.0, 0.0}, 0, 0, true}, // right
{"L5 5L10 0L5 -5z", Point{5.0, 5.0}, 0, 0, true}, // top
{"L5 5L10 0L5 -5z", Point{5.0, -5.0}, 0, 0, true}, // bottom
{"M10 0A5 5 0 0 0 0 0A5 5 0 0 0 10 0z", Point{5.0, 0.0}, 1, -1, false}, // mid
{"M10 0A5 5 0 0 0 0 0A5 5 0 0 0 10 0z", Point{0.0, 0.0}, 1, 0, true}, // left
{"M10 0A5 5 0 0 0 0 0A5 5 0 0 0 10 0z", Point{10.0, 0.0}, 0, 0, true}, // right
{"M10 0A5 5 0 0 1 0 0A5 5 0 0 1 10 0z", Point{5.0, 0.0}, 1, 1, false}, // mid
{"M10 0A5 5 0 0 1 0 0A5 5 0 0 1 10 0z", Point{0.0, 0.0}, 1, 0, true}, // left
{"M10 0A5 5 0 0 1 0 0A5 5 0 0 1 10 0z", Point{10.0, 0.0}, 0, 0, true}, // right
// cross twice
{"L10 10L10 -10L-10 10L-10 -10z", Point{0.0, 0.0}, 1, 0, true},
{"L10 10L10 -10L-10 10L-10 -10z", Point{-1.0, 0.0}, 3, 1, false},
{"L10 10L10 -10L-10 10L20 40L20 -40L-10 -10z", Point{0.0, 0.0}, 2, 0, true},
{"L10 10L10 -10L-10 10L20 40L20 -40L-10 -10z", Point{1.0, 0.0}, 2, -2, false},
{"L10 10L10 -10L-10 10L20 40L20 -40L-10 -10z", Point{-1.0, 0.0}, 4, 0, false},
}
for _, tt := range tts {
t.Run(fmt.Sprint(tt.p, " at ", tt.pos), func(t *testing.T) {
p := MustParseSVGPath(tt.p)
crossings, boundary1 := p.Crossings(tt.pos.X, tt.pos.Y)
windings, boundary2 := p.Windings(tt.pos.X, tt.pos.Y)
test.T(t, []any{crossings, windings, boundary1, boundary2}, []any{tt.crossings, tt.windings, tt.boundary, tt.boundary})
})
}
}
func TestPathCCW(t *testing.T) {
var tts = []struct {
p string
ccw bool
}{
{"L10 0L10 10z", true},
{"L10 0L10 -10z", false},
{"L10 0", true},
{"M10 0", true},
{"Q0 -1 1 0", true},
{"Q0 1 1 0", false},
{"C0 -1 1 -1 1 0", true},
{"C0 1 1 1 1 0", false},
{"A1 1 0 0 1 2 0", true},
{"A1 1 0 0 0 2 0", false},
// parallel on right-most endpoint
//{"L10 0L5 0L2.5 5z", true}, // TODO: overlapping segments?
{"L0 5L5 5A5 5 0 0 1 0 0z", false},
{"Q0 5 5 5A5 5 0 0 1 0 0z", false},
{"M0 10L0 5L5 5A5 5 0 0 0 0 10z", true},
{"M0 10Q0 5 5 5A5 5 0 0 0 0 10z", true},
// bugs
{"M0.31191406250000003 0.9650390625L0.3083984375 0.9724609375L0.3013671875 0.9724609375L0.29824218750000003 0.9646484375z", true},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
test.T(t, MustParseSVGPath(tt.p).CCW(), tt.ccw)
})
}
}
func TestPathFilling(t *testing.T) {
var tts = []struct {
p string
filling []bool
rule FillRule
}{
{"M0 0", []bool{}, NonZero},
{"L10 10z", []bool{true}, NonZero},
{"C5 0 10 5 10 10z", []bool{true}, NonZero},
{"C0 5 5 10 10 10z", []bool{true}, NonZero},
{"Q10 0 10 10z", []bool{true}, NonZero},
{"Q0 10 10 10z", []bool{true}, NonZero},
{"A10 10 0 0 1 10 10z", []bool{true}, NonZero},
{"A10 10 0 0 0 10 10z", []bool{true}, NonZero},
// subpaths
{"L10 0L10 10L0 10zM2 2L8 2L8 8L2 8z", []bool{true, true}, NonZero}, // outer CCW,inner CCW
{"L10 0L10 10L0 10zM2 2L8 2L8 8L2 8z", []bool{true, false}, EvenOdd}, // outer CCW,inner CCW
{"L10 0L10 10L0 10zM2 2L2 8L8 8L8 2z", []bool{true, false}, NonZero}, // outer CCW,inner CW
{"L10 0L10 10L0 10zM2 2L2 8L8 8L8 2z", []bool{true, false}, EvenOdd}, // outer CCW,inner CW
{"L10 10L0 20zM2 4L8 10L2 16z", []bool{true, true}, NonZero}, // outer CCW,inner CW
{"L10 10L0 20zM2 4L8 10L2 16z", []bool{true, false}, EvenOdd}, // outer CCW,inner CW
{"L10 10L0 20zM2 4L2 16L8 10z", []bool{true, false}, NonZero}, // outer CCW,inner CCW
{"L10 10L0 20zM2 4L2 16L8 10z", []bool{true, false}, EvenOdd}, // outer CCW,inner CCW
// paths touch at ray
{"L10 10L0 20zM2 4L10 10L2 16z", []bool{true, true}, NonZero}, // inside
{"L10 10L0 20zM2 4L10 10L2 16z", []bool{true, false}, EvenOdd}, // inside
{"L10 10L0 20zM2 4L2 16L10 10z", []bool{true, false}, NonZero}, // inside
{"L10 10L0 20zM2 4L2 16L10 10z", []bool{true, false}, EvenOdd}, // inside
//{"L10 10L0 20zM2 2L2 18L10 10z", []bool{true, false}, NonZero}, // inside // TODO
{"L10 10L0 20zM-1 -2L-1 22L10 10z", []bool{false, true}, NonZero}, // encapsulates
//{"L10 10L0 20zM-2 -2L-2 22L10 10z", []bool{false, true}, NonZero}, // encapsulates // TODO
{"L10 10L0 20zM20 0L10 10L20 20z", []bool{true, true}, NonZero}, // outside
{"L10 10zM2 2L8 8z", []bool{true, true}, NonZero}, // zero-area overlap
{"L10 10zM10 0L5 5L20 10z", []bool{true, true}, NonZero}, // outside
// equal
{"L10 -10L20 0L10 10zL10 -10L20 0L10 10z", []bool{true, true}, NonZero},
{"L10 -10L20 0L10 10zA10 10 0 0 1 20 0A10 10 0 0 1 0 0z", []bool{true, true}, NonZero},
//{"L10 -10L20 0L10 10zA10 10 0 0 0 20 0A10 10 0 0 0 0 0z", []bool{false, true}, NonZero}, // TODO
//{"L10 -10L20 0L10 10zQ10 0 10 10Q10 0 20 0Q10 0 10 -10Q10 0 0 0z", []bool{true, false}, NonZero}, // TODO
// open
{"L10 10L0 20", []bool{true}, NonZero},
{"L10 10L0 20M0 -5L0 5L-5 0z", []bool{true, true}, NonZero},
{"L10 10L0 20M0 -5L0 5L5 0z", []bool{true, true}, NonZero},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
filling := MustParseSVGPath(tt.p).Filling(tt.rule)
test.T(t, filling, tt.filling)
})
}
}
func TestPathBounds(t *testing.T) {
var tts = []struct {
p string
bounds Rect
}{
{"", Rect{}},
{"Q50 100 100 0", Rect{0, 0, 100, 50}},
{"Q100 50 0 100", Rect{0, 0, 50, 100}},
{"Q0 0 100 0", Rect{0, 0, 100, 0}},
{"Q100 0 100 0", Rect{0, 0, 100, 0}},
{"Q100 0 100 100", Rect{0, 0, 100, 100}},
{"C0 0 100 0 100 0", Rect{0, 0, 100, 0}},
{"C0 100 100 100 100 0", Rect{0, 0, 100, 75}},
{"C0 0 100 90 100 0", Rect{0, 0, 100, 40}},
{"C0 90 100 0 100 0", Rect{0, 0, 100, 40}},
{"C100 100 0 100 100 0", Rect{0, 0, 100, 75}},
{"C66.667 0 100 33.333 100 100", Rect{0, 0, 100, 100}},
{"M3.1125 1.7812C3.4406 1.7812 3.5562 1.5938 3.4578 1.2656", Rect{3.1125, 1.2656, 3.1125 + 0.379252, 1.2656 + 0.515599}},
{"A100 100 0 0 0 100 100", Rect{0, 0, 100, 100}},
{"A50 100 90 0 0 200 0", Rect{0, 0, 200, 50}},
{"A100 100 0 1 0 -100 100", Rect{-200, -100, 0, 100}}, // hit xmin, ymin
{"A100 100 0 1 1 -100 100", Rect{-100, 0, 100, 200}}, // hit xmax, ymax
}
origEpsilon := Epsilon
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
Epsilon = origEpsilon
bounds := MustParseSVGPath(tt.p).Bounds()
Epsilon = 1e-6
test.T(t, bounds, tt.bounds)
})
}
Epsilon = origEpsilon
}
// for quadratic Bézier use https://www.wolframalpha.com/input/?i=length+of+the+curve+%7Bx%3D2*(1-t)*t*50.00+%2B+t%5E2*100.00,+y%3D2*(1-t)*t*66.67+%2B+t%5E2*0.00%7D+from+0+to+1
// for cubic Bézier use https://www.wolframalpha.com/input/?i=length+of+the+curve+%7Bx%3D3*(1-t)%5E2*t*0.00+%2B+3*(1-t)*t%5E2*100.00+%2B+t%5E3*100.00,+y%3D3*(1-t)%5E2*t*66.67+%2B+3*(1-t)*t%5E2*66.67+%2B+t%5E3*0.00%7D+from+0+to+1
// for ellipse use https://www.wolframalpha.com/input/?i=length+of+the+curve+%7Bx%3D10.00*cos(t),+y%3D20.0*sin(t)%7D+from+0+to+pi
func TestPathLength(t *testing.T) {
var tts = []struct {
p string
length float64
}{
{"M10 0z", 0.0},
{"Q50 66.67 100 0", 124.533},
{"Q100 0 100 0", 100.0000},
{"C0 66.67 100 66.67 100 0", 158.5864},
{"C0 0 100 66.67 100 0", 125.746},
{"C0 0 100 0 100 0", 100.0000},
{"C100 66.67 0 66.67 100 0", 143.9746},
{"A10 20 0 0 0 20 0", 48.4422},
{"A10 20 0 0 1 20 0", 48.4422},
{"A10 20 0 1 0 20 0", 48.4422},
{"A10 20 0 1 1 20 0", 48.4422},
{"A10 20 30 0 0 20 0", 31.4622},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
length := MustParseSVGPath(tt.p).Length()
if math.Abs(tt.length-length)/length > 0.01 {
test.Fail(t, length, "!=", tt.length, "±1%")
}
})
}
}
func TestPathTransform(t *testing.T) {
var tts = []struct {
p string
m Matrix
r string
}{
{"L10 0Q15 10 20 0C23 10 27 10 30 0z", Identity.Translate(0, 100), "M0 100L10 100Q15 110 20 100C23 110 27 110 30 100z"},
{"A10 10 0 0 0 20 0", Identity.Translate(0, 10), "M0 10A10 10 0 0 0 20 10"},
{"A10 10 0 0 0 20 0", Identity.Scale(1, -1), "A10 10 0 0 1 20 0"},
{"A10 5 0 0 0 20 0", Identity.Rotate(270), "A10 5 90 0 0 0 -20"},
{"A10 10 0 0 0 20 0", Identity.Rotate(120).Scale(1, -2), "A20 10 30 0 1 -10 17.3205080757"},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
test.T(t, MustParseSVGPath(tt.p).Transform(tt.m), MustParseSVGPath(tt.r))
})
}
}
func TestPathReplace(t *testing.T) {
line := func(p0, p1 Point) *Path {
p := &Path{}
p.MoveTo(p0.X, p0.Y)
p.LineTo(p1.X, p1.Y-5.0)
return p
}
quad := func(p0, p1, p2 Point) *Path {
p := &Path{}
p.MoveTo(p0.X, p0.Y)
p.LineTo(p2.X, p2.Y)
return p
}
cube := func(p0, p1, p2, p3 Point) *Path {
p := &Path{}
p.MoveTo(p0.X, p0.Y)
p.LineTo(p3.X, p3.Y)
return p
}
arc := func(p0 Point, rx, ry, phi float64, largeArc, sweep bool, p1 Point) *Path {
p := &Path{}
p.MoveTo(p0.X, p0.Y)
p.ArcTo(rx, ry, phi, !largeArc, sweep, p1.X, p1.Y)
return p
}
var tts = []struct {
orig string
res string
line func(Point, Point) *Path
quad func(Point, Point, Point) *Path
cube func(Point, Point, Point, Point) *Path
arc func(Point, float64, float64, float64, bool, bool, Point) *Path
}{
{"C0 10 10 10 10 0L30 0", "L30 0", nil, quad, cube, nil},
{"M20 0L30 0C0 10 10 10 10 0", "M20 0L30 0L10 0", nil, quad, cube, nil},
{"M10 0L20 0Q25 10 20 10A5 5 0 0 0 30 10z", "M10 0L20 -5L20 10A5 5 0 1 0 30 10L10 -5z", line, quad, cube, arc},
{"L10 0L0 5z", "L10 -5L10 0L0 0L0 5L0 -5z", line, nil, nil, nil},
}
for _, tt := range tts {
t.Run(tt.orig, func(t *testing.T) {
p := MustParseSVGPath(tt.orig)
test.T(t, p.replace(tt.line, tt.quad, tt.cube, tt.arc), MustParseSVGPath(tt.res))
})
}
}
func TestPathMarkers(t *testing.T) {
start := MustParseSVGPath("L1 0L0 1z")
mid := MustParseSVGPath("M-1 0A1 1 0 0 0 1 0z")
end := MustParseSVGPath("L-1 0L0 1z")
var tts = []struct {
p string
rs []string
}{
{"M10 0", []string{"M10 0L11 0L10 1z"}},
{"M10 0L20 10", []string{"M10 0L11 0L10 1z", "M20 10L19 10L20 11z"}},
{"L10 0L20 10", []string{"L1 0L0 1z", "M9 0A1 1 0 0 0 11 0z", "M20 10L19 10L20 11z"}},
{"L10 0L20 10z", []string{"L1 0L0 1z", "M9 0A1 1 0 0 0 11 0z", "M19 10A1 1 0 0 0 21 10z", "L-1 0L0 1z"}},
{"M10 0L20 10M30 0L40 10", []string{"M10 0L11 0L10 1z", "M19 10A1 1 0 0 0 21 10z", "M29 0A1 1 0 0 0 31 0z", "M40 10L39 10L40 11z"}},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
p := MustParseSVGPath(tt.p)
ps := p.Markers(start, mid, end, false)
if len(ps) != len(tt.rs) {
origs := []string{}
for _, p := range ps {
origs = append(origs, p.String())
}
test.T(t, strings.Join(origs, "\n"), strings.Join(tt.rs, "\n"))
} else {
for i, p := range ps {
test.T(t, p, MustParseSVGPath(tt.rs[i]))
}
}
})
}
}
func TestPathMarkersAligned(t *testing.T) {
start := MustParseSVGPath("L1 0L0 1z")
mid := MustParseSVGPath("M-1 0A1 1 0 0 0 1 0z")
end := MustParseSVGPath("L-1 0L0 1z")
var tts = []struct {
p string
rs []string
}{
{"M10 0", []string{"M10 0L11 0L10 1z"}},
{"M10 0L20 10", []string{"M10 0L10.707 0.707L9.293 0.707z", "M20 10L19.293 9.293L19.293 10.707z"}},
{"L10 0L20 10", []string{"L1 0L0 1z", "M9.076 -0.383A1 1 0 0 0 10.924 0.383z", "M20 10L19.293 9.293L19.293 10.707z"}},
{"L10 0L20 10z", []string{"L0.230 -0.973L0.973 0.230z", "M9.076 -0.383A1 1 0 0 0 10.924 0.383z", "M20.585 9.189A1 1 0 0 0 19.415 10.811z", "L-0.230 0.973L0.973 0.230z"}},
{"M10 0L20 10M30 0L40 10", []string{"M10 0L10.707 0.707L9.293 0.707z", "M19.293 9.293A1 1 0 0 0 20.707 10.707z", "M29.293 -0.707A1 1 0 0 0 30.707 0.707z", "M40 10L39.293 9.293L39.293 10.707z"}},
{"Q0 10 10 10Q20 10 20 0", []string{"L0 1L-1 0z", "M9 10A1 1 0 0 0 11 10z", "M20 0L20 1L21 0z"}},
{"C0 6.66667 3.33333 10 10 10C16.66667 10 20 6.66667 20 0", []string{"L0 1L-1 0z", "M9 10A1 1 0 0 0 11 10z", "M20 0L20 1L21 0z"}},
{"A10 10 0 0 0 10 10A10 10 0 0 0 20 0", []string{"L0 1L-1 0z", "M9 10A1 1 0 0 0 11 10z", "M20 0L20 1L21 0z"}},
}
origEpsilon := Epsilon
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
Epsilon = origEpsilon
p := MustParseSVGPath(tt.p)
ps := p.Markers(start, mid, end, true)
Epsilon = 1e-3
if len(ps) != len(tt.rs) {
origs := []string{}
for _, p := range ps {
origs = append(origs, p.String())
}
test.T(t, strings.Join(origs, "\n"), strings.Join(tt.rs, "\n"))
} else {
for i, p := range ps {
test.T(t, p, MustParseSVGPath(tt.rs[i]))
}
}
})
}
Epsilon = origEpsilon
}
func TestPathSplit(t *testing.T) {
var tts = []struct {
p string
rs []string
}{
{"M5 5L6 6z", []string{"M5 5L6 6z"}},
{"L5 5M10 10L20 20z", []string{"L5 5", "M10 10L20 20z"}},
{"L5 5zL10 10", []string{"L5 5z", "L10 10"}},
{"M5 5L15 5zL10 10zL20 20", []string{"M5 5L15 5z", "M5 5L10 10z", "M5 5L20 20"}},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
p := MustParseSVGPath(tt.p)
ps := p.Split()
if len(ps) != len(tt.rs) {
origs := []string{}
for _, p := range ps {
origs = append(origs, p.String())
}
test.T(t, strings.Join(origs, "\n"), strings.Join(tt.rs, "\n"))
} else {
for i, p := range ps {
test.T(t, p, MustParseSVGPath(tt.rs[i]))
}
}
})
}
ps := (&Path{[]float64{MoveToCmd, 5.0, 5.0, MoveToCmd, MoveToCmd, 10.0, 10.0, MoveToCmd, CloseCmd, 10.0, 10.0, CloseCmd}}).Split()
test.T(t, ps[0].String(), "M5 5")
test.T(t, ps[1].String(), "M10 10z")
}
func TestPathSplitAt(t *testing.T) {
var tts = []struct {
p string
d []float64
rs []string
}{
{"L4 3L8 0z", []float64{}, []string{"L4 3L8 0z"}},
{"M2 0L4 3Q10 10 20 0C20 10 30 10 30 0A10 10 0 0 0 50 0z", []float64{0.0}, []string{"M2 0L4 3Q10 10 20 0C20 10 30 10 30 0A10 10 0 0 0 50 0L2 0"}},
{"L4 3L8 0z", []float64{0.0, 5.0, 10.0, 18.0}, []string{"L4 3", "M4 3L8 0", "M8 0L0 0"}},
{"L4 3L8 0z", []float64{5.0, 20.0}, []string{"L4 3", "M4 3L8 0L0 0"}},
{"L4 3L8 0z", []float64{2.5, 7.5, 14.0}, []string{"L2 1.5", "M2 1.5L4 3L6 1.5", "M6 1.5L8 0L4 0", "M4 0L0 0"}},
{"Q10 10 20 0", []float64{11.477858}, []string{"Q5 5 10 5", "M10 5Q15 5 20 0"}},
{"C0 10 20 10 20 0", []float64{13.947108}, []string{"C0 5 5 7.5 10 7.5", "M10 7.5C15 7.5 20 5 20 0"}},
{"A10 10 0 0 1 -20 0", []float64{15.707963}, []string{"A10 10 0 0 1 -10 10", "M-10 10A10 10 0 0 1 -20 0"}},
{"A10 10 0 0 0 20 0", []float64{15.707963}, []string{"A10 10 0 0 0 10 10", "M10 10A10 10 0 0 0 20 0"}},
{"A10 10 0 1 0 2.9289 -7.0711", []float64{15.707963}, []string{"A10 10 0 0 0 10.024 9.9999", "M10.024 9.9999A10 10 0 1 0 2.9289 -7.0711"}},
}
origEpsilon := Epsilon
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
Epsilon = origEpsilon
p := MustParseSVGPath(tt.p)
ps := p.SplitAt(tt.d...)
Epsilon = 1e-3
if len(ps) != len(tt.rs) {
origs := []string{}
for _, p := range ps {
origs = append(origs, p.String())
}
test.T(t, strings.Join(origs, "\n"), strings.Join(tt.rs, "\n"))
} else {
for i, p := range ps {
test.T(t, p, MustParseSVGPath(tt.rs[i]))
}
}
})
}
Epsilon = origEpsilon
}
func TestDashCanonical(t *testing.T) {
var tts = []struct {
origOffset float64
origDashes []float64
offset float64
dashes []float64
}{
{0.0, []float64{0.0}, 0.0, []float64{0.0}},
{0.0, []float64{-1.0}, 0.0, []float64{0.0}},
{0.0, []float64{2.0, 0.0}, 0.0, []float64{}},
{0.0, []float64{0.0, 2.0}, 0.0, []float64{0.0}},
{0.0, []float64{0.0, 2.0, 0.0}, -2.0, []float64{2.0}},
{0.0, []float64{0.0, 2.0, 3.0, 0.0}, -2.0, []float64{3.0, 2.0}},
{0.0, []float64{0.0, 2.0, 3.0, 1.0, 0.0}, -2.0, []float64{3.0, 1.0, 2.0}},
{0.0, []float64{0.0, 1.0, 2.0}, -1.0, []float64{3.0}},
{0.0, []float64{0.0, 1.0, 2.0, 4.0}, -1.0, []float64{2.0, 5.0}},
{0.0, []float64{2.0, 1.0, 0.0}, 1.0, []float64{3.0}},
{0.0, []float64{4.0, 2.0, 1.0, 0.0}, 1.0, []float64{5.0, 2.0}},
{0.0, []float64{1.0, 0.0, 2.0}, 0.0, []float64{3.0}},
{0.0, []float64{1.0, 0.0, 2.0, 2.0, 0.0, 1.0}, 0.0, []float64{3.0}},
{0.0, []float64{2.0, 0.0, -1.0}, 0.0, []float64{1.0}},
{0.0, []float64{1.0, 0.0, 2.0, 0.0, 3.0, 0.0}, 0.0, []float64{}},
{0.0, []float64{0.0, 1.0, 0.0, 2.0, 0.0, 3.0}, 0.0, []float64{0.0}},
}
for _, tt := range tts {
t.Run(fmt.Sprintf("%v +%v", tt.origDashes, tt.origOffset), func(t *testing.T) {
offset, dashes := dashCanonical(tt.origOffset, tt.origDashes)
diff := offset != tt.offset || len(dashes) != len(tt.dashes)
if !diff {
for i := 0; i < len(tt.dashes); i++ {
if dashes[i] != tt.dashes[i] {
diff = true
break
}
}
}
if diff {
test.Fail(t, fmt.Sprintf("%v +%v != %v +%v", dashes, offset, tt.dashes, tt.offset))
}
})
}
}
func TestPathDash(t *testing.T) {
var tts = []struct {
p string
offset float64
d []float64
dashes string
}{
{"", 0.0, []float64{0.0}, ""},
{"L10 0", 0.0, []float64{}, "L10 0"},
{"L10 0", 0.0, []float64{2.0}, "L2 0M4 0L6 0M8 0L10 0"},
{"L10 0", 0.0, []float64{2.0, 1.0}, "L2 0M3 0L5 0M6 0L8 0M9 0L10 0"},
{"L10 0", 1.0, []float64{2.0, 1.0}, "L1 0M2 0L4 0M5 0L7 0M8 0L10 0"},
{"L10 0", -1.0, []float64{2.0, 1.0}, "M1 0L3 0M4 0L6 0M7 0L9 0"},
{"L10 0", 2.0, []float64{2.0, 1.0}, "M1 0L3 0M4 0L6 0M7 0L9 0"},
{"L10 0", 5.0, []float64{2.0, 1.0}, "M1 0L3 0M4 0L6 0M7 0L9 0"},
{"L10 0L20 0", 0.0, []float64{15.0}, "L10 0L15 0"},
{"L10 0L20 0", 15.0, []float64{15.0}, "M15 0L20 0"},
{"L10 0L10 10L0 10z", 0.0, []float64{10.0}, "L10 0M10 10L0 10"},
{"L10 0L10 10L0 10z", 0.0, []float64{15.0}, "M0 10L0 0L10 0L10 5"},
{"M10 0L20 0L20 10L10 10z", 0.0, []float64{15.0}, "M10 10L10 0L20 0L20 5"},
{"L10 0M0 10L10 10", 0.0, []float64{8.0}, "L8 0M0 10L8 10"},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
test.T(t, MustParseSVGPath(tt.p).Dash(tt.offset, tt.d...), MustParseSVGPath(tt.dashes))
})
}
}
func TestPathReverse(t *testing.T) {
var tts = []struct {
p string
r string
}{
{"", ""},
{"M5 5", "M5 5"},
{"M5 5z", "M5 5z"},
{"M5 5L5 10L10 5", "M10 5L5 10L5 5"},
{"M5 5L5 10L10 5z", "M5 5L10 5L5 10z"},
{"M5 5L5 10L10 5M10 10L10 20L20 10z", "M10 10L20 10L10 20zM10 5L5 10L5 5"},
{"M5 5L5 10L10 5zM10 10L10 20L20 10z", "M10 10L20 10L10 20zM5 5L10 5L5 10z"},
{"M5 5Q10 10 15 5", "M15 5Q10 10 5 5"},
{"M5 5Q10 10 15 5z", "M5 5L15 5Q10 10 5 5z"},
{"M5 5C5 10 10 10 10 5", "M10 5C10 10 5 10 5 5"},
{"M5 5C5 10 10 10 10 5z", "M5 5L10 5C10 10 5 10 5 5z"},
{"M5 5A2.5 5 0 0 0 10 5", "M10 5A5 2.5 90 0 1 5 5"}, // bottom-half of ellipse along y
{"M5 5A2.5 5 0 0 1 10 5", "M10 5A5 2.5 90 0 0 5 5"},
{"M5 5A2.5 5 0 1 0 10 5", "M10 5A5 2.5 90 1 1 5 5"},
{"M5 5A2.5 5 0 1 1 10 5", "M10 5A5 2.5 90 1 0 5 5"},
{"M5 5A5 2.5 90 0 0 10 5", "M10 5A5 2.5 90 0 1 5 5"}, // same shape
{"M5 5A2.5 5 0 0 0 10 5z", "M5 5L10 5A5 2.5 90 0 1 5 5z"},
{"L0 5L5 5", "M5 5L0 5L0 0"},
{"L-1 5L5 5z", "L5 5L-1 5z"},
{"Q0 5 5 5", "M5 5Q0 5 0 0"},
{"Q0 5 5 5z", "L5 5Q0 5 0 0z"},
{"C0 5 5 5 5 0", "M5 0C5 5 0 5 0 0"},
{"C0 5 5 5 5 0z", "L5 0C5 5 0 5 0 0z"},
{"A2.5 5 0 0 0 5 0", "M5 0A5 2.5 90 0 1 0 0"},
{"A2.5 5 0 0 0 5 0z", "L5 0A5 2.5 90 0 1 0 0z"},
{"M5 5L10 10zL15 10", "M15 10L5 5M5 5L10 10z"},
{"M5 5L10 10zM0 0L15 10", "M15 10L0 0M5 5L10 10z"},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
test.T(t, MustParseSVGPath(tt.p).Reverse(), MustParseSVGPath(tt.r))
})
}
}
func TestPathParseSVGPath(t *testing.T) {
var tts = []struct {
p string
r string
}{
{"M10 0L20 0H30V10C40 10 50 10 50 0Q55 10 60 0A5 5 0 0 0 70 0Z", "M10 0L20 0L30 0L30 10C40 10 50 10 50 0Q55 10 60 0A5 5 0 0 0 70 0z"},
{"m10 0l10 0h10v10c10 0 20 0 20 -10q5 10 10 0a5 5 0 0 0 10 0z", "M10 0L20 0L30 0L30 10C40 10 50 10 50 0Q55 10 60 0A5 5 0 0 0 70 0z"},
{"C0 10 10 10 10 0S20 -10 20 0", "C0 10 10 10 10 0C10 -10 20 -10 20 0"},
{"c0 10 10 10 10 0s10 -10 10 0", "C0 10 10 10 10 0C10 -10 20 -10 20 0"},
{"Q5 10 10 0T20 0", "Q5 10 10 0Q15 -10 20 0"},
{"q5 10 10 0t10 0", "Q5 10 10 0Q15 -10 20 0"},
{"A10 10 0 0 0 40 0", "A20 20 0 0 0 40 0"}, // scale ellipse
{"A10 5 90 0 0 40 0", "A40 20 90 0 0 40 0"}, // scale ellipse
{"A10 5 0 0020 0", "A10 5 0 0 0 20 0"}, // parse boolean flags
// go-fuzz
{"V0 ", ""},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
p, err := ParseSVGPath(tt.p)
test.Error(t, err)
test.T(t, p, MustParseSVGPath(tt.r))
})
}
}
func TestPathParseSVGPathErrors(t *testing.T) {
var tts = []struct {
p string
err string
}{
{"5", "bad path: path should start with command"},
{"MM", "bad path: sets of 2 numbers should follow command 'M' at position 2"},
{"A10 10 000 20 0", "bad path: largeArc and sweep flags should be 0 or 1 in command 'A' at position 12"},
{"A10 10 0 23 20 0", "bad path: largeArc and sweep flags should be 0 or 1 in command 'A' at position 10"},
// go-fuzz
{"V4-z\n0ìGßIzØ", "bad path: unknown command '-' at position 3"},
{"ae000e000e00", "bad path: sets of 7 numbers should follow command 'a' at position 2"},
{"s........----.......---------------", "bad path: sets of 4 numbers should follow command 's' at position 2"},
{"l00000000000000000000+00000000000000000000 00000000000000000000", "bad path: sets of 2 numbers should follow command 'l' at position 64"},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
_, err := ParseSVGPath(tt.p)
test.That(t, err != nil)
test.T(t, err.Error(), tt.err)
})
}
}
func TestPathToSVG(t *testing.T) {
var tts = []struct {
p string
svg string
}{
{"", ""},
{"L10 0Q15 10 20 0M20 10C20 20 30 20 30 10z", "M0 0H10Q15 10 20 0M20 10C20 20 30 20 30 10z"},
{"L10 0M20 0L30 0", "M0 0H10M20 0H30"},
{"L0 0L0 10L20 20", "M0 0V10L20 20"},
{"A5 5 0 0 1 10 0", "M0 0A5 5 0 0110 0"},
{"A10 5 90 0 0 10 0", "M0 0A5 10 0 0010 0"},
{"A10 5 90 1 0 10 0", "M0 0A5 10 0 1010 0"},
{"M20 0L20 0", ""},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
p := MustParseSVGPath(tt.p)
test.T(t, p.ToSVG(), tt.svg)
})
}
}
func TestPathToPS(t *testing.T) {
var tts = []struct {
p string
ps string
}{
{"", ""},
{"L10 0Q15 10 20 0M20 10C20 20 30 20 30 10z", "0 0 moveto 10 0 lineto 13.333333 6.6666667 16.666667 6.6666667 20 0 curveto 20 10 moveto 20 20 30 20 30 10 curveto closepath"},
{"L10 0M20 0L30 0", "0 0 moveto 10 0 lineto 20 0 moveto 30 0 lineto"},
{"A5 5 0 0 1 10 0", "0 0 moveto 5 0 5 5 180 360 0 ellipse"},
{"A10 5 90 0 0 10 0", "0 0 moveto 5 0 10 5 90 -90 90 ellipsen"},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
test.T(t, MustParseSVGPath(tt.p).ToPS(), tt.ps)
})
}
}
func TestPathToPDF(t *testing.T) {
var tts = []struct {
p string
pdf string
}{
{"", ""},
{"L10 0Q15 10 20 0M20 10C20 20 30 20 30 10z", "0 0 m 10 0 l 13.333333 6.6666667 16.666667 6.6666667 20 0 c 20 10 m 20 20 30 20 30 10 c h"},
{"L10 0M20 0L30 0", "0 0 m 10 0 l 20 0 m 30 0 l"},
}
for _, tt := range tts {
t.Run(tt.p, func(t *testing.T) {
test.T(t, MustParseSVGPath(tt.p).ToPDF(), tt.pdf)
})
}
}
func plotPathLengthParametrization(filename string, N int, speed, length func(float64) float64, tmin, tmax float64) {
Tc, totalLength := invSpeedPolynomialChebyshevApprox(N, gaussLegendre7, speed, tmin, tmax)
n := 100
realData := make(plotter.XYs, n+1)
modelData := make(plotter.XYs, n+1)
for i := 0; i < n+1; i++ {
t := tmin + (tmax-tmin)*float64(i)/float64(n)
l := totalLength * float64(i) / float64(n)
realData[i].X = length(t)
realData[i].Y = t
modelData[i].X = l
modelData[i].Y = Tc(l)
}
scatter, err := plotter.NewScatter(realData)
if err != nil {
panic(err)
}
scatter.Shape = draw.CircleGlyph{}
line, err := plotter.NewLine(modelData)
if err != nil {
panic(err)
}
line.LineStyle.Color = Red
line.LineStyle.Width = 2.0
p := plot.New()
p.X.Label.Text = "L"
p.Y.Label.Text = "t"
p.Add(scatter, line)
p.Legend.Add("real", scatter)
p.Legend.Add(fmt.Sprintf("Chebyshev N=%v", N), line)
if err := p.Save(7*vg.Inch, 4*vg.Inch, filename); err != nil {
panic(err)
}
}
func TestPathLengthParametrization(t *testing.T) {
if !testing.Verbose() {
t.SkipNow()
return
}
_ = os.Mkdir("test", 0755)
start := Point{0.0, 0.0}
cp := Point{1000.0, 0.0}
end := Point{10.0, 10.0}
speed := func(t float64) float64 {
return quadraticBezierDeriv(start, cp, end, t).Length()
}
length := func(t float64) float64 {
p0, p1, p2, _, _, _ := quadraticBezierSplit(start, cp, end, t)
return quadraticBezierLength(p0, p1, p2)
}
plotPathLengthParametrization("test/len_param_quad.png", 20, speed, length, 0.0, 1.0)
plotCube := func(name string, start, cp1, cp2, end Point) {
N := 20 + 20*cubicBezierNumInflections(start, cp1, cp2, end)
speed := func(t float64) float64 {
return cubicBezierDeriv(start, cp1, cp2, end, t).Length()
}
length := func(t float64) float64 {
p0, p1, p2, p3, _, _, _, _ := cubicBezierSplit(start, cp1, cp2, end, t)
return cubicBezierLength(p0, p1, p2, p3)
}
plotPathLengthParametrization(name, N, speed, length, 0.0, 1.0)
}
plotCube("test/len_param_cube.png", Point{0.0, 0.0}, Point{10.0, 0.0}, Point{10.0, 2.0}, Point{8.0, 2.0})
// see "Analysis of Inflection Points for Planar Cubic Bezier Curve" by Z.Zhang et al. from 2009
// https://cie.nwsuaf.edu.cn/docs/20170614173651207557.pdf
plotCube("test/len_param_cube1.png", Point{16, 467}, Point{185, 95}, Point{673, 545}, Point{810, 17})
plotCube("test/len_param_cube2.png", Point{859, 676}, Point{13, 422}, Point{781, 12}, Point{266, 425})
plotCube("test/len_param_cube3.png", Point{872, 686}, Point{11, 423}, Point{779, 13}, Point{220, 376})
plotCube("test/len_param_cube4.png", Point{819, 566}, Point{43, 18}, Point{826, 18}, Point{25, 533})
plotCube("test/len_param_cube5.png", Point{884, 574}, Point{135, 14}, Point{678, 14}, Point{14, 566})
rx, ry := 10000.0, 10.0
phi := 0.0
sweep := false
end = Point{-100.0, 10.0}
theta1, theta2 := 0.0, 0.5*math.Pi
speed = func(theta float64) float64 {
return ellipseDeriv(rx, ry, phi, sweep, theta).Length()
}
length = func(theta float64) float64 {
return ellipseLength(rx, ry, theta1, theta)
}
plotPathLengthParametrization("test/len_param_ellipse.png", 20, speed, length, theta1, theta2)
}