Add chart components 216-245; step-aware ticks, font-aware labels

Bars, lines, areas, pies, donuts, radar, histogram, scatter, bubbles,
heatmaps, gauge, bullet, funnel, waterfall, treemap, candles, box
plots, steps, rings, legend, axis, crosshair, polar area, pyramid,
spectrum bars and win-loss strips, each drawn dot by dot. Ticks follow
1-2-5 steps and print as precisely as their step needs; a label row
uses micro letters or the pixel font as a whole. Descriptions carry the
data in numbers. Bad data panics.

chart/boxplot.go

@@ -0,0 +1,70 @@
+package chart
+
+import (
+	"fmt"
+	"slices"
+	"strings"
+
+	"github.com/egoist/mygo/ui"
+
+	"git.zacharyzhang.com/ZacharyZhang-NY/8bitMyGoUI/pixel"
+)
+
+type BoxPlotOptions struct {
+	// Width and Height are dots; zeros mean 160 by 80.
+	Width, Height int
+	Slot          pixel.Slot
+}
+
+// quartile is the q-th quartile of sorted values, interpolated.
+func quartile(sorted []float64, q float64) float64 {
+	at := q * float64(len(sorted)-1)
+	i := int(at)
+	if i+1 >= len(sorted) {
+		return sorted[i]
+	}
+	return sorted[i] + (sorted[i+1]-sorted[i])*(at-float64(i))
+}
+
+// BoxPlot boxes each group's quartiles; whiskers reach its ends.
+func BoxPlot(c *ui.Context, text string, groups []Series, o BoxPlotOptions) *ui.Element {
+	k := pixel.K(c)
+	if len(groups) == 0 {
+		panic("chart: BoxPlot has no groups")
+	}
+	w, h := size("BoxPlot", o.Width, o.Height, 160, 80)
+	labels, rows := make([]string, len(groups)), make([][]float64, len(groups))
+	for i, s := range groups {
+		if len(s.Values) == 0 {
+			panic(fmt.Sprintf("chart: BoxPlot group %q is empty", s.Name))
+		}
+		labels[i], rows[i] = s.Name, slices.Sorted(slices.Values(s.Values))
+	}
+	lo, hi := span(rows...)
+	p := fit(lo, hi, w, h, labels)
+	return ui.Box(c).Size(k.D(w), k.D(h)).Role(ui.RoleImage).Label(text).Description(fives(labels, rows)).Draw(func(pt *ui.Painter, r ui.Rect) {
+		g := k.Canvas(pt, r)
+		p.grid(g, labels)
+		bw := max(3, p.w/len(groups)/2)
+		for i, row := range rows {
+			x := p.slot(i, len(groups))
+			q1, mid, q3 := p.at(quartile(row, 0.25)), p.at(quartile(row, 0.5)), p.at(quartile(row, 0.75))
+			top, bottom := p.at(row[len(row)-1]), p.at(row[0])
+			g.VLine(x, top, q3-top, pixel.Edge)
+			g.VLine(x, q1, bottom-q1+1, pixel.Edge)
+			g.HLine(x-bw/4, top, bw/2+1, pixel.Edge)
+			g.HLine(x-bw/4, bottom, bw/2+1, pixel.Edge)
+			g.Frame(x-bw/2, q3, bw, max(3, q1-q3+1), pixel.Flat, pick(groups[i].Slot, i))
+			g.HLine(x-bw/2, mid, bw, pixel.Ink)
+		}
+	})
+}
+
+// fives lists each sorted row's five-number summary.
+func fives(labels []string, rows [][]float64) string {
+	parts := make([]string, len(rows))
+	for i, row := range rows {
+		parts[i] = labels[i] + " " + nums([]float64{row[0], quartile(row, 0.25), quartile(row, 0.5), quartile(row, 0.75), row[len(row)-1]})
+	}
+	return strings.Join(parts, "; ")
+}