// 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].Rectangle.Min.X = w*vg.Length(l.XAlign) + l.XOffset
bs[i].Rectangle.Min.Y = h*vg.Length(l.YAlign) + l.YOffset
bs[i].Rectangle.Max.X = w + w*vg.Length(l.XAlign) + l.XOffset
bs[i].Rectangle.Max.Y = h + h*vg.Length(l.YAlign) + l.YOffset
}
return bs
}
// 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 (c *Canvas) FillText(sty TextStyle, x, y vg.Length, xalign, yalign float64, txt string) {
txt = strings.TrimRight(txt, "\n")
if len(txt) == 0 {
return
}
c.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)
c.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))
}
// NewWith returns a new image canvas created according to the specified
// options. The currently accepted options are UseWH,
// UseDPI, UseImage, and UseImageWithContext.
// Each of the options specifies the size of the canvas (UseWH, UseImage),
// the resolution of the canvas (UseDPI), or both (useImageWithContext).
// If size or resolution are not specified, defaults are used.
// It panics if size and resolution are overspecified (i.e., too many options are
// passed).
func NewWith(o ...option) *Canvas {
c := new(Canvas)
var g uint32
for _, opt := range o {
f := opt(c)
if g&f != 0 {
panic("incompatible options")
}
g |= f
}
if c.dpi == 0 {
c.dpi = DefaultDPI
}
if c.w == 0 { // h should also == 0.
if c.img == nil {
c.w = DefaultWidth
c.h = DefaultHeight
} else {
w := float64(c.img.Bounds().Max.X - c.img.Bounds().Min.X)
h := float64(c.img.Bounds().Max.Y - c.img.Bounds().Min.Y)
c.w = vg.Length(w/float64(c.dpi)) * vg.Inch
c.h = vg.Length(h/float64(c.dpi)) * vg.Inch
}
}
if c.img == nil {
w := c.w / vg.Inch * vg.Length(c.dpi)
h := c.h / vg.Inch * vg.Length(c.dpi)
c.img = draw.Image(image.NewRGBA(image.Rect(0, 0, int(w+0.5), int(h+0.5))))
}
if c.gc == nil {
h := float64(c.img.Bounds().Max.Y - c.img.Bounds().Min.Y)
c.gc = draw2dimg.NewGraphicContext(c.img)
c.gc.SetDPI(c.dpi)
c.gc.Scale(1, -1)
c.gc.Translate(0, -h)
}
draw.Draw(c.img, c.img.Bounds(), image.White, image.ZP, draw.Src)
c.color = []color.Color{color.Black}
vg.Initialize(c)
return c
}
// padX returns a draw.Canvas that is padded horizontally
// so that glyphs will no be clipped.
func padX(p *Plot, c draw.Canvas) draw.Canvas {
glyphs := p.GlyphBoxes(p)
l := leftMost(&c, glyphs)
xAxis := horizontalAxis{p.X}
glyphs = append(glyphs, xAxis.GlyphBoxes(p)...)
r := rightMost(&c, glyphs)
minx := c.Min.X - l.Min.X
maxx := c.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 draw.Canvas{
Canvas: vg.Canvas(c),
Rectangle: draw.Rectangle{
Min: draw.Point{X: n, Y: c.Min.Y},
Max: draw.Point{X: m, Y: c.Max.Y},
},
}
}
// padY returns a draw.Canvas that is padded vertically
// so that glyphs will no be clipped.
func padY(p *Plot, c draw.Canvas) draw.Canvas {
glyphs := p.GlyphBoxes(p)
b := bottomMost(&c, glyphs)
yAxis := verticalAxis{p.Y}
glyphs = append(glyphs, yAxis.GlyphBoxes(p)...)
t := topMost(&c, glyphs)
miny := c.Min.Y - b.Min.Y
maxy := c.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 draw.Canvas{
Canvas: vg.Canvas(c),
Rectangle: draw.Rectangle{
Min: draw.Point{Y: n, X: c.Min.X},
Max: draw.Point{Y: m, X: c.Max.X},
},
}
}
// tickLabelWidth returns the width of the widest tick mark label.
func tickLabelWidth(sty draw.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 draw.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
}
// draw draws the legend to the given draw.Canvas.
func (l *Legend) draw(c draw.Canvas) {
iconx := c.Min.X
textx := iconx + l.ThumbnailWidth + l.TextStyle.Width(" ")
xalign := 0.0
if !l.Left {
iconx = c.Max.X - l.ThumbnailWidth
textx = iconx - l.TextStyle.Width(" ")
xalign = -1
}
textx += l.XOffs
iconx += l.XOffs
enth := l.entryHeight()
y := c.Max.Y - enth
if !l.Top {
y = c.Min.Y + (enth+l.Padding)*(vg.Length(len(l.entries))-1)
}
y += l.YOffs
icon := &draw.Canvas{
Canvas: c.Canvas,
Rectangle: draw.Rectangle{
Min: draw.Point{iconx, y},
Max: draw.Point{iconx + l.ThumbnailWidth, y + enth},
},
}
for _, e := range l.entries {
for _, t := range e.thumbs {
t.Thumbnail(icon)
}
yoffs := (enth - l.TextStyle.Height(e.text)) / 2
c.FillText(l.TextStyle, textx, icon.Min.Y+yoffs, xalign, 0, e.text)
icon.Min.Y -= enth + l.Padding
icon.Max.Y -= enth + l.Padding
}
}
// At returns the subcanvas within c that corresponds to the
// tile at column x, row y.
func (ts Tiles) At(c Canvas, x, y int) Canvas {
tileH := (c.Max.Y - c.Min.Y - ts.PadTop - ts.PadBottom -
vg.Length(ts.Rows-1)*ts.PadY) / vg.Length(ts.Rows)
tileW := (c.Max.X - c.Min.X - ts.PadLeft - ts.PadRight -
vg.Length(ts.Cols-1)*ts.PadX) / vg.Length(ts.Cols)
ymax := c.Max.Y - ts.PadTop - vg.Length(y)*(ts.PadY+tileH)
ymin := ymax - tileH
xmin := c.Min.X + ts.PadLeft + vg.Length(x)*(ts.PadX+tileW)
xmax := xmin + tileW
return Canvas{
Canvas: vg.Canvas(c),
Rectangle: Rectangle{
Min: Point{X: xmin, Y: ymin},
Max: Point{X: xmax, Y: ymax},
},
}
}
func unity(f float64) vg.Length { return vg.Length(f) }
// 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 (c *Canvas) Y(y float64) vg.Length {
return vg.Length(y)*(c.Max.Y-c.Min.Y) + c.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 (c *Canvas) X(x float64) vg.Length {
return vg.Length(x)*(c.Max.X-c.Min.X) + c.Min.X
}
// RingGlyph is a glyph that draws the outline of a circle.
type RingGlyph struct{}
// DrawGlyph implements the Glyph interface.
func (RingGlyph) DrawGlyph(c *Canvas, sty GlyphStyle, pt Point) {
c.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()
c.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(c *Canvas, sty GlyphStyle, pt Point) {
c.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)
}
}
}