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op/clip: split clip operations into its own package
Signed-off-by: Elias Naur <mail@eliasnaur.com>
This commit is contained in:
Elias Naur
+297
@@ -0,0 +1,297 @@
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// SPDX-License-Identifier: Unlicense OR MIT
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package clip
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import (
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"encoding/binary"
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"image"
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"math"
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"gioui.org/f32"
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"gioui.org/internal/opconst"
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"gioui.org/internal/path"
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"gioui.org/op"
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)
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// Path constructs a Op clip path described by lines and
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// Bézier curves, where drawing outside the Path is discarded.
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// The inside-ness of a pixel is determines by the even-odd rule,
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// similar to the SVG rule of the same name.
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//
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// Path generates no garbage and can be used for dynamic paths; path
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// data is stored directly in the Ops list supplied to Begin.
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type Path struct {
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ops *op.Ops
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contour int
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pen f32.Point
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bounds f32.Rectangle
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hasBounds bool
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macro op.MacroOp
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}
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// Op sets the current clip to the intersection of
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// the existing clip with this clip.
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//
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// If you need to reset the clip to its previous values after
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// applying a Op, use op.StackOp.
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type Op struct {
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macro op.MacroOp
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bounds f32.Rectangle
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}
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func (p Op) Add(o *op.Ops) {
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p.macro.Add(o)
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data := o.Write(opconst.TypeClipLen)
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data[0] = byte(opconst.TypeClip)
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bo := binary.LittleEndian
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bo.PutUint32(data[1:], math.Float32bits(p.bounds.Min.X))
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bo.PutUint32(data[5:], math.Float32bits(p.bounds.Min.Y))
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bo.PutUint32(data[9:], math.Float32bits(p.bounds.Max.X))
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bo.PutUint32(data[13:], math.Float32bits(p.bounds.Max.Y))
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}
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// Begin the path, storing the path data and final Op into ops.
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func (p *Path) Begin(ops *op.Ops) {
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p.ops = ops
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p.macro.Record(ops)
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// Write the TypeAux opcode and a byte for marking whether the
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// path has had its MaxY filled out. If not, the gpu will fill it
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// before using it.
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data := ops.Write(2)
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data[0] = byte(opconst.TypeAux)
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}
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// MoveTo moves the pen to the given position.
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func (p *Path) Move(to f32.Point) {
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p.end()
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to = to.Add(p.pen)
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p.pen = to
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}
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// end completes the current contour.
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func (p *Path) end() {
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p.contour++
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}
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// Line moves the pen by the amount specified by delta, recording a line.
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func (p *Path) Line(delta f32.Point) {
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to := delta.Add(p.pen)
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p.lineTo(to)
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}
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func (p *Path) lineTo(to f32.Point) {
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// Model lines as degenerate quadratic Béziers.
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p.quadTo(to.Add(p.pen).Mul(.5), to)
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}
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// Quad records a quadratic Bézier from the pen to end
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// with the control point ctrl.
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func (p *Path) Quad(ctrl, to f32.Point) {
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ctrl = ctrl.Add(p.pen)
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to = to.Add(p.pen)
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p.quadTo(ctrl, to)
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}
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func (p *Path) quadTo(ctrl, to f32.Point) {
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// Zero width curves don't contribute to stenciling.
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if p.pen.X == to.X && p.pen.X == ctrl.X {
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p.pen = to
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return
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}
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bounds := f32.Rectangle{
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Min: p.pen,
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Max: to,
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}.Canon()
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// If the curve contain areas where a vertical line
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// intersects it twice, split the curve in two x monotone
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// lower and upper curves. The stencil fragment program
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// expects only one intersection per curve.
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// Find the t where the derivative in x is 0.
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v0 := ctrl.Sub(p.pen)
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v1 := to.Sub(ctrl)
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d := v0.X - v1.X
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// t = v0 / d. Split if t is in ]0;1[.
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if v0.X > 0 && d > v0.X || v0.X < 0 && d < v0.X {
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t := v0.X / d
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ctrl0 := p.pen.Mul(1 - t).Add(ctrl.Mul(t))
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ctrl1 := ctrl.Mul(1 - t).Add(to.Mul(t))
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mid := ctrl0.Mul(1 - t).Add(ctrl1.Mul(t))
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p.simpleQuadTo(ctrl0, mid)
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p.simpleQuadTo(ctrl1, to)
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if mid.X > bounds.Max.X {
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bounds.Max.X = mid.X
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}
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if mid.X < bounds.Min.X {
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bounds.Min.X = mid.X
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}
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} else {
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p.simpleQuadTo(ctrl, to)
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}
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// Find the y extremum, if any.
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d = v0.Y - v1.Y
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if v0.Y > 0 && d > v0.Y || v0.Y < 0 && d < v0.Y {
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t := v0.Y / d
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y := (1-t)*(1-t)*p.pen.Y + 2*(1-t)*t*ctrl.Y + t*t*to.Y
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if y > bounds.Max.Y {
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bounds.Max.Y = y
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}
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if y < bounds.Min.Y {
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bounds.Min.Y = y
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}
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}
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p.expand(bounds)
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}
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// Cube records a cubic Bézier from the pen through
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// two control points ending in to.
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func (p *Path) Cube(ctrl0, ctrl1, to f32.Point) {
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ctrl0 = ctrl0.Add(p.pen)
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ctrl1 = ctrl1.Add(p.pen)
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to = to.Add(p.pen)
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// Set the maximum distance proportionally to the longest side
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// of the bounding rectangle.
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hull := f32.Rectangle{
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Min: p.pen,
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Max: ctrl0,
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}.Canon().Add(ctrl1).Add(to)
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l := hull.Dx()
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if h := hull.Dy(); h > l {
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l = h
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}
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p.approxCubeTo(0, l*0.001, ctrl0, ctrl1, to)
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}
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// approxCube approximates a cubic Bézier by a series of quadratic
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// curves.
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func (p *Path) approxCubeTo(splits int, maxDist float32, ctrl0, ctrl1, to f32.Point) int {
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// The idea is from
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// https://caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html
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// where a quadratic approximates a cubic by eliminating its t³ term
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// from its polynomial expression anchored at the starting point:
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//
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// P(t) = pen + 3t(ctrl0 - pen) + 3t²(ctrl1 - 2ctrl0 + pen) + t³(to - 3ctrl1 + 3ctrl0 - pen)
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//
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// The control point for the new quadratic Q1 that shares starting point, pen, with P is
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//
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// C1 = (3ctrl0 - pen)/2
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//
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// The reverse cubic anchored at the end point has the polynomial
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//
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// P'(t) = to + 3t(ctrl1 - to) + 3t²(ctrl0 - 2ctrl1 + to) + t³(pen - 3ctrl0 + 3ctrl1 - to)
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//
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// The corresponding quadratic Q2 that shares the end point, to, with P has control
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// point
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//
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// C2 = (3ctrl1 - to)/2
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//
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// The combined quadratic Bézier, Q, shares both start and end points with its cubic
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// and use the midpoint between the two curves Q1 and Q2 as control point:
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//
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// C = (3ctrl0 - pen + 3ctrl1 - to)/4
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c := ctrl0.Mul(3).Sub(p.pen).Add(ctrl1.Mul(3)).Sub(to).Mul(1.0 / 4.0)
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const maxSplits = 32
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if splits >= maxSplits {
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p.quadTo(c, to)
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return splits
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}
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// The maximum distance between the cubic P and its approximation Q given t
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// can be shown to be
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//
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// d = sqrt(3)/36*|to - 3ctrl1 + 3ctrl0 - pen|
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//
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// To save a square root, compare d² with the squared tolerance.
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v := to.Sub(ctrl1.Mul(3)).Add(ctrl0.Mul(3)).Sub(p.pen)
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d2 := (v.X*v.X + v.Y*v.Y) * 3 / (36 * 36)
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if d2 <= maxDist*maxDist {
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p.quadTo(c, to)
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return splits
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}
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// De Casteljau split the curve and approximate the halves.
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t := float32(0.5)
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c0 := p.pen.Add(ctrl0.Sub(p.pen).Mul(t))
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c1 := ctrl0.Add(ctrl1.Sub(ctrl0).Mul(t))
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c2 := ctrl1.Add(to.Sub(ctrl1).Mul(t))
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c01 := c0.Add(c1.Sub(c0).Mul(t))
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c12 := c1.Add(c2.Sub(c1).Mul(t))
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c0112 := c01.Add(c12.Sub(c01).Mul(t))
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splits++
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splits = p.approxCubeTo(splits, maxDist, c0, c01, c0112)
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splits = p.approxCubeTo(splits, maxDist, c12, c2, to)
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return splits
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}
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func (p *Path) expand(b f32.Rectangle) {
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if !p.hasBounds {
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p.hasBounds = true
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inf := float32(math.Inf(+1))
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p.bounds = f32.Rectangle{
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Min: f32.Point{X: inf, Y: inf},
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Max: f32.Point{X: -inf, Y: -inf},
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}
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}
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p.bounds = p.bounds.Union(b)
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}
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func (p *Path) vertex(cornerx, cornery int16, ctrl, to f32.Point) {
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v := path.Vertex{
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CornerX: cornerx,
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CornerY: cornery,
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FromX: p.pen.X,
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FromY: p.pen.Y,
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CtrlX: ctrl.X,
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CtrlY: ctrl.Y,
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ToX: to.X,
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ToY: to.Y,
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}
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data := p.ops.Write(path.VertStride)
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bo := binary.LittleEndian
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data[0] = byte(uint16(v.CornerX))
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data[1] = byte(uint16(v.CornerX) >> 8)
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data[2] = byte(uint16(v.CornerY))
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data[3] = byte(uint16(v.CornerY) >> 8)
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// Put the contour index in MaxY.
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bo.PutUint32(data[4:], uint32(p.contour))
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bo.PutUint32(data[8:], math.Float32bits(v.FromX))
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bo.PutUint32(data[12:], math.Float32bits(v.FromY))
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bo.PutUint32(data[16:], math.Float32bits(v.CtrlX))
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bo.PutUint32(data[20:], math.Float32bits(v.CtrlY))
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bo.PutUint32(data[24:], math.Float32bits(v.ToX))
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bo.PutUint32(data[28:], math.Float32bits(v.ToY))
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}
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func (p *Path) simpleQuadTo(ctrl, to f32.Point) {
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// NW.
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p.vertex(-1, 1, ctrl, to)
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// NE.
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p.vertex(1, 1, ctrl, to)
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// SW.
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p.vertex(-1, -1, ctrl, to)
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// SE.
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p.vertex(1, -1, ctrl, to)
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p.pen = to
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}
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// End the path and return a clip operation that represents it.
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func (p *Path) End() Op {
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p.end()
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p.macro.Stop()
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return Op{
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macro: p.macro,
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bounds: p.bounds,
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}
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}
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// Rect returns the clip area of a pixel aligned rectangular area.
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func Rect(r image.Rectangle) Op {
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return Op{bounds: toRectF(r)}
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}
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func toRectF(r image.Rectangle) f32.Rectangle {
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return f32.Rectangle{
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Min: f32.Point{X: float32(r.Min.X), Y: float32(r.Min.Y)},
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Max: f32.Point{X: float32(r.Max.X), Y: float32(r.Max.Y)},
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}
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}
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@@ -0,0 +1,16 @@
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// SPDX-License-Identifier: Unlicense OR MIT
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/*
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Package clip provides operations for clipping paint operations.
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Drawing outside the current clip area is ignored.
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The current clip is initially the infinite set. An Op sets the clip
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to the intersection of the current clip and the clip area it
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represents. If you need to reset the current clip to its value
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before applying an Op, use op.StackOp.
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General clipping areas are constructed with Path. Simpler special
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cases such as rectangular clip areas also exist as convenient
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constructors.
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*/
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package clip
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