// Approximate a circular arc using multiple
// cubic Bézier curves, one for each π/2 segment.
//
// This is from:
// http://hansmuller-flex.blogspot.com/2011/04/approximating-circular-arc-with-cubic.html
func arc(p *pdf.Path, comp vg.PathComp) {
x0 := comp.X + comp.Radius*vg.Length(math.Cos(comp.Start))
y0 := comp.Y + comp.Radius*vg.Length(math.Sin(comp.Start))
p.Line(pdfPoint(x0, y0))
a1 := comp.Start
end := a1 + comp.Angle
sign := 1.0
if end < a1 {
sign = -1.0
}
left := math.Abs(comp.Angle)
// Square root of the machine epsilon for IEEE 64-bit floating
// point values. This is the equality threshold recommended
// in Numerical Recipes, if I recall correctly—it's small enough.
const epsilon = 1.4901161193847656e-08
for left > epsilon {
a2 := a1 + sign*math.Min(math.Pi/2, left)
partialArc(p, comp.X, comp.Y, comp.Radius, a1, a2)
left -= math.Abs(a2 - a1)
a1 = a2
}
}
// Height returns the height of the text when using
// the given font.
func (sty TextStyle) Height(txt string) vg.Length {
nl := textNLines(txt)
if nl == 0 {
return vg.Length(0)
}
e := sty.Font.Extents()
return e.Height*vg.Length(nl-1) + e.Ascent
}
// GlyphBoxes returns a slice of GlyphBoxes,
// one for each of the labels, implementing the
// plot.GlyphBoxer interface.
func (l *Labels) GlyphBoxes(p *plot.Plot) []plot.GlyphBox {
bs := make([]plot.GlyphBox, len(l.Labels))
for i, label := range l.Labels {
bs[i].X = p.X.Norm(l.XYs[i].X)
bs[i].Y = p.Y.Norm(l.XYs[i].Y)
w := l.Width(label)
h := l.Height(label)
bs[i].Rect.Min.X = w*vg.Length(l.XAlign) + l.XOffset
bs[i].Rect.Min.Y = h*vg.Length(l.YAlign) + l.YOffset
bs[i].Rect.Size.X = w
bs[i].Rect.Size.Y = h
}
return bs
}
// draw draws the legend to the given DrawArea.
func (l *Legend) draw(da DrawArea) {
iconx := da.Min.X
textx := iconx + l.ThumbnailWidth + l.TextStyle.Width(" ")
xalign := 0.0
if !l.Left {
iconx = da.Max().X - l.ThumbnailWidth
textx = iconx - l.TextStyle.Width(" ")
xalign = -1
}
textx += l.XOffs
iconx += l.XOffs
enth := l.entryHeight()
y := da.Max().Y - enth
if !l.Top {
y = da.Min.Y + (enth+l.Padding)*(vg.Length(len(l.entries))-1)
}
y += l.YOffs
icon := &DrawArea{
Canvas: da.Canvas,
Rect: Rect{Min: Point{iconx, y}, Size: Point{l.ThumbnailWidth, enth}},
}
for _, e := range l.entries {
for _, t := range e.thumbs {
t.Thumbnail(icon)
}
yoffs := (enth - l.TextStyle.Height(e.text)) / 2
da.FillText(l.TextStyle, textx, icon.Min.Y+yoffs, xalign, 0, e.text)
icon.Min.Y -= enth + l.Padding
}
}
// FillText fills lines of text in the draw area.
// The text is offset by its width times xalign and
// its height times yalign. x and y give the bottom
// left corner of the text befor e it is offset.
func (da *DrawArea) FillText(sty TextStyle, x, y vg.Length, xalign, yalign float64, txt string) {
txt = strings.TrimRight(txt, "\n")
if len(txt) == 0 {
return
}
da.SetColor(sty.Color)
ht := sty.Height(txt)
y += ht*vg.Length(yalign) - sty.Font.Extents().Ascent
nl := textNLines(txt)
for i, line := range strings.Split(txt, "\n") {
xoffs := vg.Length(xalign) * sty.Font.Width(line)
n := vg.Length(nl - i)
da.FillString(sty.Font, x+xoffs, y+n*sty.Font.Size, line)
}
}
// radius returns the radius of a bubble by linear interpolation.
func (bs *Bubbles) radius(z float64) vg.Length {
rng := bs.MaxRadius - bs.MinRadius
if bs.MaxZ == bs.MinZ {
return rng/2 + bs.MinRadius
}
d := (z - bs.MinZ) / (bs.MaxZ - bs.MinZ)
return vg.Length(d)*rng + bs.MinRadius
}
// Approximate a circular arc of fewer than π/2
// radians with cubic Bézier curve.
func partialArc(p *pdf.Path, x, y, r vg.Length, a1, a2 float64) {
a := (a2 - a1) / 2
x4 := r * vg.Length(math.Cos(a))
y4 := r * vg.Length(math.Sin(a))
x1 := x4
y1 := -y4
const k = 0.5522847498 // some magic constant
f := k * vg.Length(math.Tan(a))
x2 := x1 + f*y4
y2 := y1 + f*x4
x3 := x2
y3 := -y2
// Rotate and translate points into position.
ar := a + a1
sinar := vg.Length(math.Sin(ar))
cosar := vg.Length(math.Cos(ar))
x2r := x2*cosar - y2*sinar + x
y2r := x2*sinar + y2*cosar + y
x3r := x3*cosar - y3*sinar + x
y3r := x3*sinar + y3*cosar + y
x4 = r*vg.Length(math.Cos(a2)) + x
y4 = r*vg.Length(math.Sin(a2)) + y
p.Curve(pdfPoint(x2r, y2r), pdfPoint(x3r, y3r), pdfPoint(x4, y4))
}
// padY returns a DrawArea that is padded vertically
// so that glyphs will no be clipped.
func padY(p *Plot, da DrawArea) DrawArea {
glyphs := p.GlyphBoxes(p)
b := bottomMost(&da, glyphs)
yAxis := verticalAxis{p.Y}
glyphs = append(glyphs, yAxis.GlyphBoxes(p)...)
t := topMost(&da, glyphs)
miny := da.Min.Y - b.Min.Y
maxy := da.Max().Y - (t.Min.Y + t.Size.Y)
by := vg.Length(b.Y)
ty := vg.Length(t.Y)
n := (by*maxy - ty*miny) / (by - ty)
m := ((by-1)*maxy - ty*miny + miny) / (by - ty)
return DrawArea{
Canvas: vg.Canvas(da),
Rect: Rect{
Min: Point{Y: n, X: da.Min.X},
Size: Point{Y: m - n, X: da.Size.X},
},
}
}
// padX returns a DrawArea that is padded horizontally
// so that glyphs will no be clipped.
func padX(p *Plot, da DrawArea) DrawArea {
glyphs := p.GlyphBoxes(p)
l := leftMost(&da, glyphs)
xAxis := horizontalAxis{p.X}
glyphs = append(glyphs, xAxis.GlyphBoxes(p)...)
r := rightMost(&da, glyphs)
minx := da.Min.X - l.Min.X
maxx := da.Max().X - (r.Min.X + r.Size.X)
lx := vg.Length(l.X)
rx := vg.Length(r.X)
n := (lx*maxx - rx*minx) / (lx - rx)
m := ((lx-1)*maxx - rx*minx + minx) / (lx - rx)
return DrawArea{
Canvas: vg.Canvas(da),
Rect: Rect{
Min: Point{X: n, Y: da.Min.Y},
Size: Point{X: m - n, Y: da.Size.Y},
},
}
}
// tickLabelWidth returns the width of the widest tick mark label.
func tickLabelWidth(sty TextStyle, ticks []Tick) vg.Length {
maxWidth := vg.Length(0)
for _, t := range ticks {
if t.IsMinor() {
continue
}
w := sty.Width(t.Label)
if w > maxWidth {
maxWidth = w
}
}
return maxWidth
}
// tickLabelHeight returns height of the tick mark labels.
func tickLabelHeight(sty TextStyle, ticks []Tick) vg.Length {
maxHeight := vg.Length(0)
for _, t := range ticks {
if t.IsMinor() {
continue
}
h := sty.Height(t.Label)
if h > maxHeight {
maxHeight = h
}
}
return maxHeight
}
// Y returns the value of x, given in the unit range,
// in the drawing coordinates of this draw area.
// A value of 0, for example, will return the minimum
// y value of the draw area and a value of 1 will
// return the maximum.
func (da *DrawArea) Y(y float64) vg.Length {
return vg.Length(y)*(da.Max().Y-da.Min.Y) + da.Min.Y
}
// X returns the value of x, given in the unit range,
// in the drawing coordinates of this draw area.
// A value of 0, for example, will return the minimum
// x value of the draw area and a value of 1 will
// return the maximum.
func (da *DrawArea) X(x float64) vg.Length {
return vg.Length(x)*(da.Max().X-da.Min.X) + da.Min.X
}
// RingGlyph is a glyph that draws the outline of a circle.
type RingGlyph struct{}
// DrawGlyph implements the Glyph interface.
func (RingGlyph) DrawGlyph(da *DrawArea, sty GlyphStyle, pt Point) {
da.SetLineStyle(LineStyle{Color: sty.Color, Width: vg.Points(0.5)})
var p vg.Path
p.Move(pt.X+sty.Radius, pt.Y)
p.Arc(pt.X, pt.Y, sty.Radius, 0, 2*math.Pi)
p.Close()
da.Stroke(p)
}
const (
cosπover4 = vg.Length(.707106781202420)
sinπover6 = vg.Length(.500000000025921)
cosπover6 = vg.Length(.866025403769473)
)
// SquareGlyph is a glyph that draws the outline of a square.
type SquareGlyph struct{}
// DrawGlyph implements the Glyph interface.
func (SquareGlyph) DrawGlyph(da *DrawArea, sty GlyphStyle, pt Point) {
da.SetLineStyle(LineStyle{Color: sty.Color, Width: vg.Points(0.5)})
x := (sty.Radius-sty.Radius*cosπover4)/2 + sty.Radius*cosπover4
var p vg.Path
p.Move(pt.X-x, pt.Y-x)
p.Line(pt.X+x, pt.Y-x)
p.Line(pt.X+x, pt.Y+x)
func TestBubblesRadius(t *testing.T) {
b := &Bubbles{
MinRadius: vg.Length(0),
MaxRadius: vg.Length(1),
}
tests := []struct {
minz, maxz, z float64
r vg.Length
}{
{0, 0, 0, vg.Length(0.5)},
{1, 1, 1, vg.Length(0.5)},
{0, 1, 0, vg.Length(0)},
{0, 1, 1, vg.Length(1)},
{0, 1, 0.5, vg.Length(0.5)},
{0, 2, 1, vg.Length(0.5)},
{0, 4, 0, vg.Length(0)},
{0, 4, 1, vg.Length(0.25)},
{0, 4, 2, vg.Length(0.5)},
{0, 4, 3, vg.Length(0.75)},
{0, 4, 4, vg.Length(1)},
}
for _, test := range tests {
b.MinZ, b.MaxZ = test.minz, test.maxz
if r := b.radius(test.z); r != test.r {
t.Errorf("Got incorrect radius (%g) on %v", r, test)
}
}
}