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field.go
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field.go
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// Copyright ©2019 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package plotter
import (
"math"
"gonum.org/v1/plot"
"gonum.org/v1/plot/vg"
"gonum.org/v1/plot/vg/draw"
)
// FieldXY describes a two dimensional vector field where the
// X and Y coordinates are arranged on a rectangular grid.
type FieldXY interface {
// Dims returns the dimensions of the grid.
Dims() (c, r int)
// Vector returns the value of a vector field at (c, r).
// It will panic if c or r are out of bounds for the field.
Vector(c, r int) XY
// X returns the coordinate for the column at the index c.
// It will panic if c is out of bounds for the grid.
X(c int) float64
// Y returns the coordinate for the row at the index r.
// It will panic if r is out of bounds for the grid.
Y(r int) float64
}
// Field implements the Plotter interface, drawing
// a vector field of the values in the FieldXY field.
type Field struct {
FieldXY FieldXY
// DrawGlyph is the user hook to draw a field
// vector glyph. The function should draw a unit
// vector to (1, 0) on the vg.Canvas, c.
// The direction and magnitude of v can be used
// to determine properties of the glyph drawing
// but should not be used to determine size or
// directions of the glyph.
//
// If DrawGlyph is nil, a simple arrow will be
// drawn.
DrawGlyph func(c vg.Canvas, v XY)
// LineStyle is the style of the line used to
// render vectors if DrawGlyph is nil.
LineStyle draw.LineStyle
// max define the dynamic range of the field.
max float64
}
// NewField creates a new vector field plotter.
func NewField(f FieldXY) *Field {
max := math.Inf(-1)
c, r := f.Dims()
for i := 0; i < c; i++ {
for j := 0; j < r; j++ {
v := f.Vector(i, j)
d := math.Hypot(v.X, v.Y)
if math.IsNaN(d) {
continue
}
max = math.Max(max, d)
}
}
return &Field{
FieldXY: f,
LineStyle: DefaultLineStyle,
max: max,
}
}
// Plot implements the Plot method of the plot.Plotter interface.
func (f *Field) Plot(c draw.Canvas, plt *plot.Plot) {
c.Push()
c.SetLineStyle(f.LineStyle)
defer c.Pop()
trX, trY := plt.Transforms(&c)
cols, rows := f.FieldXY.Dims()
for i := 0; i < cols; i++ {
var right, left float64
switch i {
case 0:
right = (f.FieldXY.X(1) - f.FieldXY.X(0)) / 2
left = -right
case cols - 1:
right = (f.FieldXY.X(cols-1) - f.FieldXY.X(cols-2)) / 2
left = -right
default:
right = (f.FieldXY.X(i+1) - f.FieldXY.X(i)) / 2
left = -(f.FieldXY.X(i) - f.FieldXY.X(i-1)) / 2
}
for j := 0; j < rows; j++ {
var up, down float64
switch j {
case 0:
up = (f.FieldXY.Y(1) - f.FieldXY.Y(0)) / 2
down = -up
case rows - 1:
up = (f.FieldXY.Y(rows-1) - f.FieldXY.Y(rows-2)) / 2
down = -up
default:
up = (f.FieldXY.Y(j+1) - f.FieldXY.Y(j)) / 2
down = -(f.FieldXY.Y(j) - f.FieldXY.Y(j-1)) / 2
}
x, y := trX(f.FieldXY.X(i)+left), trY(f.FieldXY.Y(j)+down)
dx, dy := trX(f.FieldXY.X(i)+right), trY(f.FieldXY.Y(j)+up)
if !c.Contains(vg.Point{X: x, Y: y}) || !c.Contains(vg.Point{X: dx, Y: dy}) {
continue
}
c.Push()
c.Translate(vg.Point{X: (x + dx) / 2, Y: (y + dy) / 2})
v := f.FieldXY.Vector(i, j)
c.Rotate(math.Atan2(v.Y, v.X))
s := math.Hypot(v.X, v.Y) / (2 * f.max)
v.X *= s
v.Y *= s
c.Scale(s*float64(dx-x), s*float64(dy-y))
if f.DrawGlyph == nil {
drawVector(c, v)
} else {
f.DrawGlyph(c, v)
}
c.Pop()
}
}
}
func drawVector(c vg.Canvas, v XY) {
if math.Hypot(v.X, v.Y) == 0 {
return
}
// TODO(kortschak): Improve this arrow.
var pa vg.Path
pa.Move(vg.Point{})
pa.Line(vg.Point{X: 1, Y: 0})
pa.Close()
c.Stroke(pa)
}
// DataRange implements the DataRange method
// of the plot.DataRanger interface.
func (f *Field) DataRange() (xmin, xmax, ymin, ymax float64) {
c, r := f.FieldXY.Dims()
switch c {
case 1: // Make a unit length when there is no neighbour.
xmax = 0.5
xmin = -0.5
default:
xmax = f.FieldXY.X(c-1) + (f.FieldXY.X(c-1)-f.FieldXY.X(c-2))/2
xmin = f.FieldXY.X(0) - (f.FieldXY.X(1)-f.FieldXY.X(0))/2
}
switch r {
case 1: // Make a unit length when there is no neighbour.
ymax = 0.5
ymin = -0.5
default:
ymax = f.FieldXY.Y(r-1) + (f.FieldXY.Y(r-1)-f.FieldXY.Y(r-2))/2
ymin = f.FieldXY.Y(0) - (f.FieldXY.Y(1)-f.FieldXY.Y(0))/2
}
return xmin, xmax, ymin, ymax
}
// GlyphBoxes implements the GlyphBoxes method
// of the plot.GlyphBoxer interface.
func (f *Field) GlyphBoxes(plt *plot.Plot) []plot.GlyphBox {
c, r := f.FieldXY.Dims()
b := make([]plot.GlyphBox, 0, r*c)
for i := 0; i < c; i++ {
for j := 0; j < r; j++ {
b = append(b, plot.GlyphBox{
X: plt.X.Norm(f.FieldXY.X(i)),
Y: plt.Y.Norm(f.FieldXY.Y(j)),
Rectangle: vg.Rectangle{
Min: vg.Point{X: -5, Y: -5},
Max: vg.Point{X: +5, Y: +5},
},
})
}
}
return b
}