5792b75123
Fix bug where the String representation of a Fix32 representing minus one quarter was "0:064" instead of "-0:064". R=r, rsc, rog, nigeltao_gnome CC=golang-dev http://codereview.appspot.com/2275043
321 lines
7.7 KiB
Go
321 lines
7.7 KiB
Go
// Copyright 2010 The Freetype-Go Authors. All rights reserved.
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// Use of this source code is governed by your choice of either the
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// FreeType License or the GNU General Public License version 2 (or
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// any later version), both of which can be found in the LICENSE file.
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package raster
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import (
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"fmt"
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"math"
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)
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// A Fix32 is a 24.8 fixed point number.
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type Fix32 int32
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// A Fix64 is a 48.16 fixed point number.
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type Fix64 int64
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// String returns a human-readable representation of a 24.8 fixed point number.
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// For example, the number one-and-a-quarter becomes "1:064".
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func (x Fix32) String() string {
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if x < 0 {
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x = -x
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return fmt.Sprintf("-%d:%03d", int32(x/256), int32(x%256))
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}
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return fmt.Sprintf("%d:%03d", int32(x/256), int32(x%256))
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}
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// String returns a human-readable representation of a 48.16 fixed point number.
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// For example, the number one-and-a-quarter becomes "1:16384".
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func (x Fix64) String() string {
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if x < 0 {
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x = -x
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return fmt.Sprintf("-%d:%05d", int64(x/65536), int64(x%65536))
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}
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return fmt.Sprintf("%d:%05d", int64(x/65536), int64(x%65536))
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}
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// maxAbs returns the maximum of abs(a) and abs(b).
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func maxAbs(a, b Fix32) Fix32 {
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if a < 0 {
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a = -a
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}
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if b < 0 {
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b = -b
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}
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if a < b {
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return b
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}
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return a
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}
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// A Point represents a two-dimensional point or vector, in 24.8 fixed point
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// format.
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type Point struct {
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X, Y Fix32
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}
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// String returns a human-readable representation of a Point.
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func (p Point) String() string {
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return "(" + p.X.String() + ", " + p.Y.String() + ")"
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}
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// Add returns the vector p + q.
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func (p Point) Add(q Point) Point {
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return Point{p.X + q.X, p.Y + q.Y}
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}
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// Sub returns the vector p - q.
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func (p Point) Sub(q Point) Point {
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return Point{p.X - q.X, p.Y - q.Y}
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}
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// Mul returns the vector k * p.
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func (p Point) Mul(k Fix32) Point {
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return Point{p.X * k / 256, p.Y * k / 256}
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}
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// Neg returns the vector -p, or equivalently p rotated by 180 degrees.
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func (p Point) Neg() Point {
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return Point{-p.X, -p.Y}
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}
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// Dot returns the dot product p·q.
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func (p Point) Dot(q Point) Fix64 {
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px, py := int64(p.X), int64(p.Y)
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qx, qy := int64(q.X), int64(q.Y)
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return Fix64(px*qx + py*qy)
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}
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// Len returns the length of the vector p.
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func (p Point) Len() Fix32 {
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// TODO(nigeltao): use fixed point math.
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x := float64(p.X)
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y := float64(p.Y)
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return Fix32(math.Sqrt(x*x + y*y))
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}
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// Norm returns the vector p normalized to the given length, or the zero Point
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// if p is degenerate.
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func (p Point) Norm(length Fix32) Point {
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d := p.Len()
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if d == 0 {
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return Point{0, 0}
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}
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s, t := int64(length), int64(d)
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x := int64(p.X) * s / t
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y := int64(p.Y) * s / t
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return Point{Fix32(x), Fix32(y)}
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}
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// Rot45CW returns the vector p rotated clockwise by 45 degrees.
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// Note that the Y-axis grows downwards, so {1, 0}.Rot45CW is {1/√2, 1/√2}.
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func (p Point) Rot45CW() Point {
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// 181/256 is approximately 1/√2, or sin(π/4).
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px, py := int64(p.X), int64(p.Y)
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qx := (+px - py) * 181 / 256
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qy := (+px + py) * 181 / 256
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return Point{Fix32(qx), Fix32(qy)}
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}
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// Rot90CW returns the vector p rotated clockwise by 90 degrees.
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// Note that the Y-axis grows downwards, so {1, 0}.Rot90CW is {0, 1}.
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func (p Point) Rot90CW() Point {
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return Point{-p.Y, p.X}
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}
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// Rot135CW returns the vector p rotated clockwise by 135 degrees.
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// Note that the Y-axis grows downwards, so {1, 0}.Rot135CW is {-1/√2, 1/√2}.
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func (p Point) Rot135CW() Point {
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// 181/256 is approximately 1/√2, or sin(π/4).
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px, py := int64(p.X), int64(p.Y)
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qx := (-px - py) * 181 / 256
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qy := (+px - py) * 181 / 256
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return Point{Fix32(qx), Fix32(qy)}
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}
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// Rot45CCW returns the vector p rotated counter-clockwise by 45 degrees.
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// Note that the Y-axis grows downwards, so {1, 0}.Rot45CCW is {1/√2, -1/√2}.
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func (p Point) Rot45CCW() Point {
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// 181/256 is approximately 1/√2, or sin(π/4).
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px, py := int64(p.X), int64(p.Y)
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qx := (+px + py) * 181 / 256
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qy := (-px + py) * 181 / 256
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return Point{Fix32(qx), Fix32(qy)}
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}
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// Rot90CCW returns the vector p rotated counter-clockwise by 90 degrees.
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// Note that the Y-axis grows downwards, so {1, 0}.Rot90CCW is {0, -1}.
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func (p Point) Rot90CCW() Point {
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return Point{p.Y, -p.X}
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}
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// Rot135CCW returns the vector p rotated counter-clockwise by 135 degrees.
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// Note that the Y-axis grows downwards, so {1, 0}.Rot135CCW is {-1/√2, -1/√2}.
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func (p Point) Rot135CCW() Point {
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// 181/256 is approximately 1/√2, or sin(π/4).
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px, py := int64(p.X), int64(p.Y)
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qx := (-px + py) * 181 / 256
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qy := (-px - py) * 181 / 256
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return Point{Fix32(qx), Fix32(qy)}
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}
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// An Adder accumulates points on a curve.
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type Adder interface {
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// Start starts a new curve at the given point.
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Start(a Point)
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// Add1 adds a linear segment to the current curve.
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Add1(b Point)
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// Add2 adds a quadratic segment to the current curve.
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Add2(b, c Point)
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// Add3 adds a cubic segment to the current curve.
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Add3(b, c, d Point)
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}
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// A Path is a sequence of curves, and a curve is a start point followed by a
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// sequence of linear, quadratic or cubic segments.
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type Path []Fix32
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// String returns a human-readable representation of a Path.
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func (p Path) String() string {
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s := ""
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for i := 0; i < len(p); {
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if i != 0 {
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s += " "
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}
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switch p[i] {
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case 0:
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s += "S0" + fmt.Sprint([]Fix32(p[i+1:i+3]))
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i += 4
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case 1:
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s += "A1" + fmt.Sprint([]Fix32(p[i+1:i+3]))
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i += 4
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case 2:
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s += "A2" + fmt.Sprint([]Fix32(p[i+1:i+5]))
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i += 6
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case 3:
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s += "A3" + fmt.Sprint([]Fix32(p[i+1:i+7]))
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i += 8
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default:
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panic("freetype/raster: bad path")
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}
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}
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return s
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}
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// grow adds n elements to p.
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func (p *Path) grow(n int) {
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n += len(*p)
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if n > cap(*p) {
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old := *p
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*p = make([]Fix32, n, 2*n+8)
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copy(*p, old)
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return
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}
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*p = (*p)[0:n]
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}
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// Clear cancels any previous calls to p.Start or p.AddXxx.
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func (p *Path) Clear() {
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*p = (*p)[0:0]
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}
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// Start starts a new curve at the given point.
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func (p *Path) Start(a Point) {
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n := len(*p)
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p.grow(4)
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(*p)[n] = 0
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(*p)[n+1] = a.X
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(*p)[n+2] = a.Y
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(*p)[n+3] = 0
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}
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// Add1 adds a linear segment to the current curve.
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func (p *Path) Add1(b Point) {
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n := len(*p)
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p.grow(4)
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(*p)[n] = 1
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(*p)[n+1] = b.X
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(*p)[n+2] = b.Y
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(*p)[n+3] = 1
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}
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// Add2 adds a quadratic segment to the current curve.
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func (p *Path) Add2(b, c Point) {
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n := len(*p)
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p.grow(6)
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(*p)[n] = 2
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(*p)[n+1] = b.X
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(*p)[n+2] = b.Y
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(*p)[n+3] = c.X
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(*p)[n+4] = c.Y
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(*p)[n+5] = 2
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}
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// Add3 adds a cubic segment to the current curve.
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func (p *Path) Add3(b, c, d Point) {
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n := len(*p)
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p.grow(8)
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(*p)[n] = 3
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(*p)[n+1] = b.X
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(*p)[n+2] = b.Y
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(*p)[n+3] = c.X
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(*p)[n+4] = c.Y
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(*p)[n+5] = d.X
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(*p)[n+6] = d.Y
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(*p)[n+7] = 3
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}
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// AddPath adds the Path q to p.
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func (p *Path) AddPath(q Path) {
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n, m := len(*p), len(q)
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p.grow(m)
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copy((*p)[n:n+m], q)
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}
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// AddStroke adds a stroked Path.
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func (p *Path) AddStroke(q Path, width Fix32, cr Capper, jr Joiner) {
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Stroke(p, q, width, cr, jr)
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}
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// firstPoint returns the first point in a non-empty Path.
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func (p Path) firstPoint() Point {
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return Point{p[1], p[2]}
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}
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// lastPoint returns the last point in a non-empty Path.
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func (p Path) lastPoint() Point {
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return Point{p[len(p)-3], p[len(p)-2]}
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}
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// addPathReversed adds q reversed to p.
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// For example, if q consists of a linear segment from A to B followed by a
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// quadratic segment from B to C to D, then the values of q looks like:
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// index: 01234567890123
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// value: 0AA01BB12CCDD2
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// So, when adding q backwards to p, we want to Add2(C, B) followed by Add1(A).
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func addPathReversed(p Adder, q Path) {
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if len(q) == 0 {
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return
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}
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i := len(q) - 1
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for {
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switch q[i] {
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case 0:
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return
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case 1:
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i -= 4
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p.Add1(Point{q[i-2], q[i-1]})
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case 2:
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i -= 6
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p.Add2(Point{q[i+2], q[i+3]}, Point{q[i-2], q[i-1]})
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case 3:
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i -= 8
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p.Add3(Point{q[i+4], q[i+5]}, Point{q[i+2], q[i+3]}, Point{q[i-2], q[i-1]})
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default:
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panic("freetype/raster: bad path")
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}
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}
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}
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