From 315f87896b32d4e1dfe19aac51a1265aafd18c0e Mon Sep 17 00:00:00 2001 From: Hajime Hoshi Date: Tue, 6 Jul 2021 03:26:52 +0900 Subject: [PATCH] =?UTF-8?q?vector:=20Better=20interpolation=20of=20B=C3=A9?= =?UTF-8?q?zier=20curves?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Updates #844 --- vector/path.go | 96 ++++++++++++++++++++++++++++++++------------------ 1 file changed, 62 insertions(+), 34 deletions(-) diff --git a/vector/path.go b/vector/path.go index dfd4024e7..fa36495a3 100644 --- a/vector/path.go +++ b/vector/path.go @@ -18,8 +18,6 @@ package vector import ( - "math" - "github.com/hajimehoshi/ebiten/v2" ) @@ -51,46 +49,76 @@ func (p *Path) LineTo(x, y float32) { p.cur = point{x: x, y: y} } -// nseg returns a number of segments based on the given two points (x0, y0) and (x1, y1). -func nseg(x0, y0, x1, y1 float32) int { - distx := x1 - x0 - if distx < 0 { - distx = -distx - } - disty := y1 - y0 - if disty < 0 { - disty = -disty - } - dist := distx - if dist < disty { - dist = disty - } - - return int(math.Ceil(float64(dist))) -} - // QuadTo adds a quadratic Bézier curve to the path. func (p *Path) QuadTo(cpx, cpy, x, y float32) { - // TODO: Split more appropriate number of segments. - c := p.cur - num := nseg(c.x, c.y, x, y) - for t := float32(0.0); t <= 1; t += 1.0 / float32(num) { - xf := (1-t)*(1-t)*c.x + 2*t*(1-t)*cpx + t*t*x - yf := (1-t)*(1-t)*c.y + 2*t*(1-t)*cpy + t*t*y - p.LineTo(xf, yf) + p.quadTo(cpx, cpy, x, y, 0) +} + +// isPointCloseToSegment detects the distance between a segment (x0, y0)-(x1, y1) and a point (x, y) is less than allow. +func isPointCloseToSegment(x, y, x0, y0, x1, y1 float32, allow float32) bool { + // Line passing through (x0, y0) and (x1, y1) in the form of ax + by + c = 0 + a := y1 - y0 + b := -(x1 - x0) + c := (x1-x0)*y0 - (y1-y0)*x0 + + // The distance between a line ax+by+c=0 and (x0, y0) is + // |ax0 + by0 + c| / √(a² + b²) + return allow*allow*(a*a+b*b) > (a*x+b*y+c)*(a*x+b*y+c) +} + +func (p *Path) quadTo(x1, y1, x2, y2 float32, level int) { + if level > 10 { + return } + + x0 := p.cur.x + y0 := p.cur.y + if isPointCloseToSegment(x1, y1, x0, y0, x2, y2, 1) { + p.LineTo(x2, y2) + return + } + + x01 := (x0 + x1) / 2 + y01 := (y0 + y1) / 2 + x12 := (x1 + x2) / 2 + y12 := (y1 + y2) / 2 + x012 := (x01 + x12) / 2 + y012 := (y01 + y12) / 2 + p.quadTo(x01, y01, x012, y012, level+1) + p.quadTo(x12, y12, x2, y2, level+1) } // CubicTo adds a cubic Bézier curve to the path. func (p *Path) CubicTo(cp0x, cp0y, cp1x, cp1y, x, y float32) { - // TODO: Split more appropriate number of segments. - c := p.cur - num := nseg(c.x, c.y, x, y) - for t := float32(0.0); t <= 1; t += 1.0 / float32(num) { - xf := (1-t)*(1-t)*(1-t)*c.x + 3*(1-t)*(1-t)*t*cp0x + 3*(1-t)*t*t*cp1x + t*t*t*x - yf := (1-t)*(1-t)*(1-t)*c.y + 3*(1-t)*(1-t)*t*cp0y + 3*(1-t)*t*t*cp1y + t*t*t*y - p.LineTo(xf, yf) + p.cubicTo(cp0x, cp0y, cp1x, cp1y, x, y, 0) +} + +func (p *Path) cubicTo(x1, y1, x2, y2, x3, y3 float32, level int) { + if level > 10 { + return } + + x0 := p.cur.x + y0 := p.cur.y + if isPointCloseToSegment(x1, y1, x0, y0, x3, y3, 1) && isPointCloseToSegment(x2, y2, x0, y0, x3, y3, 1) { + p.LineTo(x3, y3) + return + } + + x01 := (x0 + x1) / 2 + y01 := (y0 + y1) / 2 + x12 := (x1 + x2) / 2 + y12 := (y1 + y2) / 2 + x23 := (x2 + x3) / 2 + y23 := (y2 + y3) / 2 + x012 := (x01 + x12) / 2 + y012 := (y01 + y12) / 2 + x123 := (x12 + x23) / 2 + y123 := (y12 + y23) / 2 + x0123 := (x012 + x123) / 2 + y0123 := (y012 + y123) / 2 + p.cubicTo(x01, y01, x012, y012, x0123, y0123, level+1) + p.cubicTo(x123, y123, x23, y23, x3, y3, level+1) } // AppendVerticesAndIndices appends vertices and indices for this path and returns them.