// SPDX-License-Identifier: Unlicense OR MIT package clip import ( "encoding/binary" "image" "math" "gioui.org/f32" "gioui.org/internal/opconst" "gioui.org/internal/ops" "gioui.org/op" ) // Op represents a clip area. Op intersects the current clip area with // itself. type Op struct { bounds image.Rectangle path PathSpec outline bool stroke StrokeStyle dashes DashSpec } func (p Op) Add(o *op.Ops) { if p.path.quads > 0 { data := o.Write(opconst.TypePathLen) data[0] = byte(opconst.TypePath) bo := binary.LittleEndian bo.PutUint32(data[1:], p.path.quads) p.path.spec.Add(o) } if p.stroke.Width > 0 { data := o.Write(opconst.TypeStrokeLen) data[0] = byte(opconst.TypeStroke) bo := binary.LittleEndian bo.PutUint32(data[1:], math.Float32bits(p.stroke.Width)) bo.PutUint32(data[5:], math.Float32bits(p.stroke.Miter)) data[9] = uint8(p.stroke.Cap) data[10] = uint8(p.stroke.Join) } if p.dashes.phase != 0 || p.dashes.size > 0 { data := o.Write(opconst.TypeDashLen) data[0] = byte(opconst.TypeDash) bo := binary.LittleEndian bo.PutUint32(data[1:], math.Float32bits(p.dashes.phase)) data[5] = p.dashes.size // FIXME(sbinet) uint16? uint32? p.dashes.spec.Add(o) } data := o.Write(opconst.TypeClipLen) data[0] = byte(opconst.TypeClip) bo := binary.LittleEndian bo.PutUint32(data[1:], uint32(p.bounds.Min.X)) bo.PutUint32(data[5:], uint32(p.bounds.Min.Y)) bo.PutUint32(data[9:], uint32(p.bounds.Max.X)) bo.PutUint32(data[13:], uint32(p.bounds.Max.Y)) if p.outline { data[17] = byte(1) } } type PathSpec struct { spec op.CallOp quads uint32 // quads is the number Bézier segments in that path. } // Path constructs a Op clip path described by lines and // Bézier curves, where drawing outside the Path is discarded. // The inside-ness of a pixel is determines by the non-zero winding rule, // similar to the SVG rule of the same name. // // Path generates no garbage and can be used for dynamic paths; path // data is stored directly in the Ops list supplied to Begin. type Path struct { ops *op.Ops contour int pen f32.Point macro op.MacroOp start f32.Point quads uint32 } // Pos returns the current pen position. func (p *Path) Pos() f32.Point { return p.pen } // Begin the path, storing the path data and final Op into ops. func (p *Path) Begin(ops *op.Ops) { p.ops = ops p.macro = op.Record(ops) // Write the TypeAux opcode data := ops.Write(opconst.TypeAuxLen) data[0] = byte(opconst.TypeAux) } // End returns a PathSpec ready to use in clipping operations. func (p *Path) End() PathSpec { c := p.macro.Stop() return PathSpec{ spec: c, quads: p.quads, } } // Move moves the pen by the amount specified by delta. func (p *Path) Move(delta f32.Point) { to := delta.Add(p.pen) p.MoveTo(to) } // MoveTo moves the pen to the specified absolute coordinate. func (p *Path) MoveTo(to f32.Point) { p.end() p.pen = to p.start = to } // end completes the current contour. func (p *Path) end() { if p.pen != p.start { p.LineTo(p.start) } p.contour++ } // Line moves the pen by the amount specified by delta, recording a line. func (p *Path) Line(delta f32.Point) { to := delta.Add(p.pen) p.LineTo(to) } // LineTo moves the pen to the absolute point specified, recording a line. func (p *Path) LineTo(to f32.Point) { // Model lines as degenerate quadratic Béziers. p.QuadTo(to.Add(p.pen).Mul(.5), to) } // Quad records a quadratic Bézier from the pen to end // with the control point ctrl. func (p *Path) Quad(ctrl, to f32.Point) { ctrl = ctrl.Add(p.pen) to = to.Add(p.pen) p.QuadTo(ctrl, to) } // QuadTo records a quadratic Bézier from the pen to end // with the control point ctrl, with absolute coordinates. func (p *Path) QuadTo(ctrl, to f32.Point) { data := p.ops.Write(ops.QuadSize + 4) bo := binary.LittleEndian bo.PutUint32(data[0:], uint32(p.contour)) ops.EncodeQuad(data[4:], ops.Quad{ From: p.pen, Ctrl: ctrl, To: to, }) p.pen = to p.quads++ } // Arc adds an elliptical arc to the path. The implied ellipse is defined // by its focus points f1 and f2. // The arc starts in the current point and ends angle radians along the ellipse boundary. // The sign of angle determines the direction; positive being counter-clockwise, // negative clockwise. func (p *Path) Arc(f1, f2 f32.Point, angle float32) { f1 = f1.Add(p.pen) f2 = f2.Add(p.pen) c, rx, ry, beg, alpha := arcFrom(f1, f2, p.pen) p.arc(alpha, c, rx, ry, beg, float64(angle)) } func dist(p1, p2 f32.Point) float64 { var ( x1 = float64(p1.X) y1 = float64(p1.Y) x2 = float64(p2.X) y2 = float64(p2.Y) dx = x2 - x1 dy = y2 - y1 ) return math.Hypot(dx, dy) } func arcFrom(f1, f2, p f32.Point) (c f32.Point, rx, ry, start, alpha float64) { c = f32.Point{ X: 0.5 * (f1.X + f2.X), Y: 0.5 * (f1.Y + f2.Y), } // semi-major axis: 2a = |PF1| + |PF2| a := 0.5 * (dist(f1, p) + dist(f2, p)) // semi-minor axis: c^2 = a^2+b^2 (c: focal distance) f := dist(f1, c) b := math.Sqrt(a*a - f*f) switch { case a > b: rx = a ry = b default: rx = b ry = a } var x float64 switch { case f1 == c || f2 == c: // degenerate case of a circle. alpha = 0 default: switch { case f1.X > c.X: x = float64(f1.X - c.X) alpha = math.Acos(x / f) case f1.X < c.X: x = float64(f2.X - c.X) alpha = math.Acos(x / f) case f1.X == c.X: // special case of a "vertical" ellipse. alpha = math.Pi / 2 if f1.Y < c.Y { alpha = -alpha } } } start = math.Acos(float64(p.X-c.X) / dist(c, p)) if c.Y > p.Y { start = -start } start -= alpha return c, rx, ry, start, alpha } // arc records an elliptical arc centered at c, with radii rx and ry, // starting at angle beg and stopping at end, in radians. // // The math is extracted from the following paper: // "Drawing an elliptical arc using polylines, quadratic or // cubic Bezier curves", L. Maisonobe // An electronic version may be found at: // http://spaceroots.org/documents/ellipse/elliptical-arc.pdf func (p *Path) arc(alpha float64, c f32.Point, rx, ry, beg, delta float64) { const n = 16 var ( θ = delta / n ref f32.Affine2D // transform from absolute frame to ellipse-based one rot f32.Affine2D // rotation matrix for each segment inv f32.Affine2D // transform from ellipse-based frame to absolute one ) ref = ref.Offset(f32.Point{}.Sub(c)) ref = ref.Rotate(f32.Point{}, float32(-alpha)) ref = ref.Scale(f32.Point{}, f32.Point{ X: float32(1 / rx), Y: float32(1 / ry), }) inv = ref.Invert() rot = rot.Rotate(f32.Point{}, float32(0.5*θ)) // Instead of invoking math.Sincos for every segment, compute a rotation // matrix once and apply for each segment. // Before applying the rotation matrix rot, transform the coordinates // to a frame centered to the ellipse (and warped into a unit circle), then rotate. // Finally, transform back into the original frame. step := func(p f32.Point) f32.Point { q := ref.Transform(p) q = rot.Transform(q) q = inv.Transform(q) return q } for i := 0; i < n; i++ { p0 := p.pen p1 := step(p0) p2 := step(p1) ctl := f32.Pt( 2*p1.X-0.5*(p0.X+p2.X), 2*p1.Y-0.5*(p0.Y+p2.Y), ) p.QuadTo(ctl, p2) } } // Cube records a cubic Bézier from the pen through // two control points ending in to. func (p *Path) Cube(ctrl0, ctrl1, to f32.Point) { if ctrl0 == (f32.Point{}) && ctrl1 == (f32.Point{}) && to == (f32.Point{}) { return } ctrl0 = ctrl0.Add(p.pen) ctrl1 = ctrl1.Add(p.pen) to = to.Add(p.pen) // Set the maximum distance proportionally to the longest side // of the bounding rectangle. hull := f32.Rectangle{ Min: p.pen, Max: ctrl0, }.Canon().Add(ctrl1).Add(to) l := hull.Dx() if h := hull.Dy(); h > l { l = h } p.approxCubeTo(0, l*0.001, ctrl0, ctrl1, to) } // approxCube approximates a cubic Bézier by a series of quadratic // curves. func (p *Path) approxCubeTo(splits int, maxDist float32, ctrl0, ctrl1, to f32.Point) int { // The idea is from // https://caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html // where a quadratic approximates a cubic by eliminating its t³ term // from its polynomial expression anchored at the starting point: // // P(t) = pen + 3t(ctrl0 - pen) + 3t²(ctrl1 - 2ctrl0 + pen) + t³(to - 3ctrl1 + 3ctrl0 - pen) // // The control point for the new quadratic Q1 that shares starting point, pen, with P is // // C1 = (3ctrl0 - pen)/2 // // The reverse cubic anchored at the end point has the polynomial // // P'(t) = to + 3t(ctrl1 - to) + 3t²(ctrl0 - 2ctrl1 + to) + t³(pen - 3ctrl0 + 3ctrl1 - to) // // The corresponding quadratic Q2 that shares the end point, to, with P has control // point // // C2 = (3ctrl1 - to)/2 // // The combined quadratic Bézier, Q, shares both start and end points with its cubic // and use the midpoint between the two curves Q1 and Q2 as control point: // // C = (3ctrl0 - pen + 3ctrl1 - to)/4 c := ctrl0.Mul(3).Sub(p.pen).Add(ctrl1.Mul(3)).Sub(to).Mul(1.0 / 4.0) const maxSplits = 32 if splits >= maxSplits { p.QuadTo(c, to) return splits } // The maximum distance between the cubic P and its approximation Q given t // can be shown to be // // d = sqrt(3)/36*|to - 3ctrl1 + 3ctrl0 - pen| // // To save a square root, compare d² with the squared tolerance. v := to.Sub(ctrl1.Mul(3)).Add(ctrl0.Mul(3)).Sub(p.pen) d2 := (v.X*v.X + v.Y*v.Y) * 3 / (36 * 36) if d2 <= maxDist*maxDist { p.QuadTo(c, to) return splits } // De Casteljau split the curve and approximate the halves. t := float32(0.5) c0 := p.pen.Add(ctrl0.Sub(p.pen).Mul(t)) c1 := ctrl0.Add(ctrl1.Sub(ctrl0).Mul(t)) c2 := ctrl1.Add(to.Sub(ctrl1).Mul(t)) c01 := c0.Add(c1.Sub(c0).Mul(t)) c12 := c1.Add(c2.Sub(c1).Mul(t)) c0112 := c01.Add(c12.Sub(c01).Mul(t)) splits++ splits = p.approxCubeTo(splits, maxDist, c0, c01, c0112) splits = p.approxCubeTo(splits, maxDist, c12, c2, to) return splits } // Close closes the path. func (p *Path) Close() { p.end() } // Outline represents the area inside of a path, according to the // non-zero winding rule. type Outline struct { Path PathSpec } // Op returns a clip operation representing the outline. func (o Outline) Op() Op { return Op{ path: o.Path, outline: true, } }