shapes.go

package canvas

import (
	"math"
)

// Line returns a line segment of from (0,0) to (x,y).
func Line(x, y float64) *Path {
	if Equal(x, 0.0) && Equal(y, 0.0) {
		return &Path{}
	}

	p := &Path{}
	p.LineTo(x, y)
	return p
}

// Arc returns a circular arc with radius r and theta0 and theta1 the angles in degrees of the ellipse (before rot is applies) between which the arc will run. If theta0 < theta1, the arc will run in a CCW direction. If the difference between theta0 and theta1 is bigger than 360 degrees, one full circle will be drawn and the remaining part of diff % 360, e.g. a difference of 810 degrees will draw one full circle and an arc over 90 degrees.
func Arc(r, theta0, theta1 float64) *Path {
	return EllipticalArc(r, r, 0.0, theta0, theta1)
}

// EllipticalArc returns an elliptical arc with radii rx and ry, with rot the counter clockwise rotation in degrees, and theta0 and theta1 the angles in degrees of the ellipse (before rot is applies) between which the arc will run. If theta0 < theta1, the arc will run in a CCW direction. If the difference between theta0 and theta1 is bigger than 360 degrees, one full circle will be drawn and the remaining part of diff % 360, e.g. a difference of 810 degrees will draw one full circle and an arc over 90 degrees.
func EllipticalArc(rx, ry, rot, theta0, theta1 float64) *Path {
	p := &Path{}
	p.Arc(rx, ry, rot, theta0, theta1)
	return p
}

// Rectangle returns a rectangle of width w and height h.
func Rectangle(w, h float64) *Path {
	if Equal(w, 0.0) || Equal(h, 0.0) {
		return &Path{}
	}

	p := &Path{}
	p.LineTo(w, 0.0)
	p.LineTo(w, h)
	p.LineTo(0.0, h)
	p.Close()
	return p
}

// RoundedRectangle returns a rectangle of width w and height h with rounded corners of radius r. A negative radius will cast the corners inwards (i.e. concave).
func RoundedRectangle(w, h, r float64) *Path {
	if Equal(w, 0.0) || Equal(h, 0.0) {
		return &Path{}
	} else if Equal(r, 0.0) {
		return Rectangle(w, h)
	}

	sweep := true
	if r < 0.0 {
		sweep = false
		r = -r
	}
	r = math.Min(r, w/2.0)
	r = math.Min(r, h/2.0)

	p := &Path{}
	p.MoveTo(0.0, r)
	p.ArcTo(r, r, 0.0, false, sweep, r, 0.0)
	p.LineTo(w-r, 0.0)
	p.ArcTo(r, r, 0.0, false, sweep, w, r)
	p.LineTo(w, h-r)
	p.ArcTo(r, r, 0.0, false, sweep, w-r, h)
	p.LineTo(r, h)
	p.ArcTo(r, r, 0.0, false, sweep, 0.0, h-r)
	p.Close()
	return p
}

// BeveledRectangle returns a rectangle of width w and height h with beveled corners at distance r from the corner.
func BeveledRectangle(w, h, r float64) *Path {
	if Equal(w, 0.0) || Equal(h, 0.0) {
		return &Path{}
	} else if Equal(r, 0.0) {
		return Rectangle(w, h)
	}

	r = math.Abs(r)
	r = math.Min(r, w/2.0)
	r = math.Min(r, h/2.0)

	p := &Path{}
	p.MoveTo(0.0, r)
	p.LineTo(r, 0.0)
	p.LineTo(w-r, 0.0)
	p.LineTo(w, r)
	p.LineTo(w, h-r)
	p.LineTo(w-r, h)
	p.LineTo(r, h)
	p.LineTo(0.0, h-r)
	p.Close()
	return p
}

// Circle returns a circle of radius r.
func Circle(r float64) *Path {
	return Ellipse(r, r)
}

// Ellipse returns an ellipse of radii rx and ry.
func Ellipse(rx, ry float64) *Path {
	if Equal(rx, 0.0) || Equal(ry, 0.0) {
		return &Path{}
	}

	p := &Path{}
	p.MoveTo(rx, 0.0)
	p.ArcTo(rx, ry, 0.0, false, true, -rx, 0.0)
	p.ArcTo(rx, ry, 0.0, false, true, rx, 0.0)
	p.Close()
	return p
}

// Triangle returns a triangle of radius r pointing upwards.
func Triangle(r float64) *Path {
	return RegularPolygon(3, r, true)
}

// RegularPolygon returns a regular polygon with radius r. It uses n vertices/edges, so when n approaches infinity this will return a path that approximates a circle. n must be 3 or more. The up boolean defines whether the first point will point upwards or downwards.
func RegularPolygon(n int, r float64, up bool) *Path {
	return RegularStarPolygon(n, 1, r, up)
}

// RegularStarPolygon returns a regular star polygon with radius r. It uses n vertices of density d. This will result in a self-intersection star in counter clockwise direction. If n/2 < d the star will be clockwise and if n and d are not coprime a regular polygon will be obtained, possible with multiple windings. n must be 3 or more and d 2 or more. The up boolean defines whether the first point will point upwards or downwards.
func RegularStarPolygon(n, d int, r float64, up bool) *Path {
	if n < 3 || d < 1 || n == d*2 || Equal(r, 0.0) {
		return &Path{}
	}

	dtheta := 2.0 * math.Pi / float64(n)
	theta0 := 0.5 * math.Pi
	if !up {
		theta0 += dtheta / 2.0
	}

	p := &Path{}
	for i := 0; i == 0 || i%n != 0; i += d {
		theta := theta0 + float64(i)*dtheta
		sintheta, costheta := math.Sincos(theta)
		if i == 0 {
			p.MoveTo(r*costheta, r*sintheta)
		} else {
			p.LineTo(r*costheta, r*sintheta)
		}
	}
	p.Close()
	return p
}

// StarPolygon returns a star polygon of n points with alternating radius R and r. The up boolean defines whether the first point will be point upwards or downwards.
func StarPolygon(n int, R, r float64, up bool) *Path {
	if n < 3 || Equal(R, 0.0) || Equal(r, 0.0) {
		return &Path{}
	}

	n *= 2
	dtheta := 2.0 * math.Pi / float64(n)
	theta0 := 0.5 * math.Pi
	if !up {
		theta0 += dtheta
	}

	p := &Path{}
	for i := 0; i < n; i++ {
		theta := theta0 + float64(i)*dtheta
		sintheta, costheta := math.Sincos(theta)
		if i == 0 {
			p.MoveTo(R*costheta, R*sintheta)
		} else if i%2 == 0 {
			p.LineTo(R*costheta, R*sintheta)
		} else {
			p.LineTo(r*costheta, r*sintheta)
		}
	}
	p.Close()
	return p
}

// Grid returns a stroked grid of width w and height h, with grid line thickness r, and the number of cells horizontally and vertically as nx and ny respectively.
func Grid(w, h float64, nx, ny int, r float64) *Path {
	if nx < 1 || ny < 1 || w <= float64(nx+1)*r || h <= float64(ny+1)*r {
		return &Path{}
	}

	p := Rectangle(w, h)
	dx, dy := (w-float64(nx+1)*r)/float64(nx), (h-float64(ny+1)*r)/float64(ny)
	cell := Rectangle(dx, dy).Reverse()
	for j := 0; j < ny; j++ {
		for i := 0; i < nx; i++ {
			x := r + float64(i)*(r+dx)
			y := r + float64(j)*(r+dy)
			p = p.Append(cell.Translate(x, y))
		}
	}
	return p
}