golang-image/draw/scale.go

// Copyright 2015 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

//go:generate go run gen.go

package draw

import (
	"image"
	"math"

	"golang.org/x/image/math/f64"
)

// Copy copies the part of the source image defined by src and sr and writes to
// the part of the destination image defined by dst and the translation of sr
// so that sr.Min translates to dp.
func Copy(dst Image, dp image.Point, src image.Image, sr image.Rectangle, opts *Options) {
	mask, mp, op := image.Image(nil), image.Point{}, Over
	if opts != nil {
		// TODO: set mask, mp and op.
	}
	dr := sr.Add(dp.Sub(sr.Min))
	DrawMask(dst, dr, src, sr.Min, mask, mp, op)
}

// Scaler scales the part of the source image defined by src and sr and writes
// to the part of the destination image defined by dst and dr.
//
// A Scaler is safe to use concurrently.
type Scaler interface {
	Scale(dst Image, dr image.Rectangle, src image.Image, sr image.Rectangle, opts *Options)
}

// Transformer transforms the part of the source image defined by src and sr
// and writes to the part of the destination image defined by dst and the
// affine transform m applied to sr.
//
// For example, if m is the matrix
//
// m00 m01 m02
// m10 m11 m12
//
// then the src-space point (sx, sy) maps to the dst-space point
// (m00*sx + m01*sy + m02, m10*sx + m11*sy + m12).
//
// A Transformer is safe to use concurrently.
type Transformer interface {
	Transform(dst Image, m *f64.Aff3, src image.Image, sr image.Rectangle, opts *Options)
}

// Options are optional parameters to Copy, Scale and Transform.
//
// A nil *Options means to use the default (zero) values of each field.
type Options struct {
	// TODO: add fields a la
	// https://groups.google.com/forum/#!topic/golang-dev/fgn_xM0aeq4
}

// Interpolator is an interpolation algorithm, when dst and src pixels don't
// have a 1:1 correspondence.
//
// Of the interpolators provided by this package:
//	- NearestNeighbor is fast but usually looks worst.
//	- CatmullRom is slow but usually looks best.
//	- ApproxBiLinear has reasonable speed and quality.
//
// The time taken depends on the size of dr. For kernel interpolators, the
// speed also depends on the size of sr, and so are often slower than
// non-kernel interpolators, especially when scaling down.
type Interpolator interface {
	Scaler
	Transformer
}

// Kernel is an interpolator that blends source pixels weighted by a symmetric
// kernel function.
type Kernel struct {
	// Support is the kernel support and must be >= 0. At(t) is assumed to be
	// zero when t >= Support.
	Support float64
	// At is the kernel function. It will only be called with t in the
	// range [0, Support).
	At func(t float64) float64
}

// Scale implements the Scaler interface.
func (q *Kernel) Scale(dst Image, dr image.Rectangle, src image.Image, sr image.Rectangle, opts *Options) {
	q.NewScaler(dr.Dx(), dr.Dy(), sr.Dx(), sr.Dy()).Scale(dst, dr, src, sr, opts)
}

// NewScaler returns a Scaler that is optimized for scaling multiple times with
// the same fixed destination and source width and height.
func (q *Kernel) NewScaler(dw, dh, sw, sh int) Scaler {
	return &kernelScaler{
		kernel:     q,
		dw:         int32(dw),
		dh:         int32(dh),
		sw:         int32(sw),
		sh:         int32(sh),
		horizontal: newDistrib(q, int32(dw), int32(sw)),
		vertical:   newDistrib(q, int32(dh), int32(sh)),
	}
}

var (
	// NearestNeighbor is the nearest neighbor interpolator. It is very fast,
	// but usually gives very low quality results. When scaling up, the result
	// will look 'blocky'.
	NearestNeighbor = Interpolator(nnInterpolator{})

	// ApproxBiLinear is a mixture of the nearest neighbor and bi-linear
	// interpolators. It is fast, but usually gives medium quality results.
	//
	// It implements bi-linear interpolation when upscaling and a bi-linear
	// blend of the 4 nearest neighbor pixels when downscaling. This yields
	// nicer quality than nearest neighbor interpolation when upscaling, but
	// the time taken is independent of the number of source pixels, unlike the
	// bi-linear interpolator. When downscaling a large image, the performance
	// difference can be significant.
	ApproxBiLinear = Interpolator(ablInterpolator{})

	// BiLinear is the tent kernel. It is slow, but usually gives high quality
	// results.
	BiLinear = &Kernel{1, func(t float64) float64 {
		return 1 - t
	}}

	// CatmullRom is the Catmull-Rom kernel. It is very slow, but usually gives
	// very high quality results.
	//
	// It is an instance of the more general cubic BC-spline kernel with parameters
	// B=0 and C=0.5. See Mitchell and Netravali, "Reconstruction Filters in
	// Computer Graphics", Computer Graphics, Vol. 22, No. 4, pp. 221-228.
	CatmullRom = &Kernel{2, func(t float64) float64 {
		if t < 1 {
			return (1.5*t-2.5)*t*t + 1
		}
		return ((-0.5*t+2.5)*t-4)*t + 2
	}}

	// TODO: a Kaiser-Bessel kernel?
)

type nnInterpolator struct{}

type ablInterpolator struct{}

type kernelScaler struct {
	kernel               *Kernel
	dw, dh, sw, sh       int32
	horizontal, vertical distrib
}

// source is a range of contribs, their inverse total weight, and that ITW
// divided by 0xffff.
type source struct {
	i, j               int32
	invTotalWeight     float64
	invTotalWeightFFFF float64
}

// contrib is the weight of a column or row.
type contrib struct {
	coord  int32
	weight float64
}

// distrib measures how source pixels are distributed over destination pixels.
type distrib struct {
	// sources are what contribs each column or row in the source image owns,
	// and the total weight of those contribs.
	sources []source
	// contribs are the contributions indexed by sources[s].i and sources[s].j.
	contribs []contrib
}

// newDistrib returns a distrib that distributes sw source columns (or rows)
// over dw destination columns (or rows).
func newDistrib(q *Kernel, dw, sw int32) distrib {
	scale := float64(sw) / float64(dw)
	halfWidth, kernelArgScale := q.Support, 1.0
	// When shrinking, broaden the effective kernel support so that we still
	// visit every source pixel.
	if scale > 1 {
		halfWidth *= scale
		kernelArgScale = 1 / scale
	}

	// Make the sources slice, one source for each column or row, and temporarily
	// appropriate its elements' fields so that invTotalWeight is the scaled
	// co-ordinate of the source column or row, and i and j are the lower and
	// upper bounds of the range of destination columns or rows affected by the
	// source column or row.
	n, sources := int32(0), make([]source, dw)
	for x := range sources {
		center := (float64(x)+0.5)*scale - 0.5
		i := int32(math.Floor(center - halfWidth))
		if i < 0 {
			i = 0
		}
		j := int32(math.Ceil(center + halfWidth))
		if j > sw {
			j = sw
			if j < i {
				j = i
			}
		}
		sources[x] = source{i: i, j: j, invTotalWeight: center}
		n += j - i
	}

	contribs := make([]contrib, 0, n)
	for k, b := range sources {
		totalWeight := 0.0
		l := int32(len(contribs))
		for coord := b.i; coord < b.j; coord++ {
			t := abs((b.invTotalWeight - float64(coord)) * kernelArgScale)
			if t >= q.Support {
				continue
			}
			weight := q.At(t)
			if weight == 0 {
				continue
			}
			totalWeight += weight
			contribs = append(contribs, contrib{coord, weight})
		}
		totalWeight = 1 / totalWeight
		sources[k] = source{
			i:                  l,
			j:                  int32(len(contribs)),
			invTotalWeight:     totalWeight,
			invTotalWeightFFFF: totalWeight / 0xffff,
		}
	}

	return distrib{sources, contribs}
}

// abs is like math.Abs, but it doesn't care about negative zero, infinities or
// NaNs.
func abs(f float64) float64 {
	if f < 0 {
		f = -f
	}
	return f
}

// ftou converts the range [0.0, 1.0] to [0, 0xffff].
func ftou(f float64) uint16 {
	i := int32(0xffff*f + 0.5)
	if i > 0xffff {
		return 0xffff
	}
	if i > 0 {
		return uint16(i)
	}
	return 0
}

// fffftou converts the range [0.0, 65535.0] to [0, 0xffff].
func fffftou(f float64) uint16 {
	i := int32(f + 0.5)
	if i > 0xffff {
		return 0xffff
	}
	if i > 0 {
		return uint16(i)
	}
	return 0
}

// invert returns the inverse of m.
//
// TODO: move this into the f64 package, once we work out the convention for
// matrix methods in that package: do they modify the receiver, take a dst
// pointer argument, or return a new value?
func invert(m *f64.Aff3) f64.Aff3 {
	m00 := +m[3*1+1]
	m01 := -m[3*0+1]
	m02 := +m[3*1+2]*m[3*0+1] - m[3*1+1]*m[3*0+2]
	m10 := -m[3*1+0]
	m11 := +m[3*0+0]
	m12 := +m[3*1+0]*m[3*0+2] - m[3*1+2]*m[3*0+0]

	det := m00*m11 - m10*m01

	return f64.Aff3{
		m00 / det,
		m01 / det,
		m02 / det,
		m10 / det,
		m11 / det,
		m12 / det,
	}
}

func matMul(p, q *f64.Aff3) f64.Aff3 {
	return f64.Aff3{
		p[3*0+0]*q[3*0+0] + p[3*0+1]*q[3*1+0],
		p[3*0+0]*q[3*0+1] + p[3*0+1]*q[3*1+1],
		p[3*0+0]*q[3*0+2] + p[3*0+1]*q[3*1+2] + p[3*0+2],
		p[3*1+0]*q[3*0+0] + p[3*1+1]*q[3*1+0],
		p[3*1+0]*q[3*0+1] + p[3*1+1]*q[3*1+1],
		p[3*1+0]*q[3*0+2] + p[3*1+1]*q[3*1+2] + p[3*1+2],
	}
}

// transformRect returns a rectangle dr that contains sr transformed by s2d.
func transformRect(s2d *f64.Aff3, sr *image.Rectangle) (dr image.Rectangle) {
	ps := [...]image.Point{
		{sr.Min.X, sr.Min.Y},
		{sr.Max.X, sr.Min.Y},
		{sr.Min.X, sr.Max.Y},
		{sr.Max.X, sr.Max.Y},
	}
	for i, p := range ps {
		sxf := float64(p.X)
		syf := float64(p.Y)
		dx := int(math.Floor(s2d[0]*sxf + s2d[1]*syf + s2d[2]))
		dy := int(math.Floor(s2d[3]*sxf + s2d[4]*syf + s2d[5]))

		// The +1 adjustments below are because an image.Rectangle is inclusive
		// on the low end but exclusive on the high end.

		if i == 0 {
			dr = image.Rectangle{
				Min: image.Point{dx + 0, dy + 0},
				Max: image.Point{dx + 1, dy + 1},
			}
			continue
		}

		if dr.Min.X > dx {
			dr.Min.X = dx
		}
		dx++
		if dr.Max.X < dx {
			dr.Max.X = dx
		}

		if dr.Min.Y > dy {
			dr.Min.Y = dy
		}
		dy++
		if dr.Max.Y < dy {
			dr.Max.Y = dy
		}
	}
	return dr
}