Merge pull request faiface#287 from cebarks/geometry-refactor

Break geometry.go & geometry_test.go into multiple smaller files

circle.go

@@ -0,0 +1,334 @@
+package pixel
+
+import (
+	"fmt"
+	"math"
+)
+
+// Circle is a 2D circle. It is defined by two properties:
+//  - Center vector
+//  - Radius float64
+type Circle struct {
+	Center Vec
+	Radius float64
+}
+
+// C returns a new Circle with the given radius and center coordinates.
+//
+// Note that a negative radius is valid.
+func C(center Vec, radius float64) Circle {
+	return Circle{
+		Center: center,
+		Radius: radius,
+	}
+}
+
+// String returns the string representation of the Circle.
+//
+//  c := pixel.C(10.1234, pixel.ZV)
+//  c.String()     // returns "Circle(10.12, Vec(0, 0))"
+//  fmt.Println(c) // Circle(10.12, Vec(0, 0))
+func (c Circle) String() string {
+	return fmt.Sprintf("Circle(%s, %.2f)", c.Center, c.Radius)
+}
+
+// Norm returns the Circle in normalized form - this sets the radius to its absolute value.
+//
+// c := pixel.C(-10, pixel.ZV)
+// c.Norm() // returns pixel.Circle{pixel.Vec{0, 0}, 10}
+func (c Circle) Norm() Circle {
+	return Circle{
+		Center: c.Center,
+		Radius: math.Abs(c.Radius),
+	}
+}
+
+// Area returns the area of the Circle.
+func (c Circle) Area() float64 {
+	return math.Pi * math.Pow(c.Radius, 2)
+}
+
+// Moved returns the Circle moved by the given vector delta.
+func (c Circle) Moved(delta Vec) Circle {
+	return Circle{
+		Center: c.Center.Add(delta),
+		Radius: c.Radius,
+	}
+}
+
+// Resized returns the Circle resized by the given delta.  The Circles center is use as the anchor.
+//
+// c := pixel.C(pixel.ZV, 10)
+// c.Resized(-5) // returns pixel.Circle{pixel.Vec{0, 0}, 5}
+// c.Resized(25) // returns pixel.Circle{pixel.Vec{0, 0}, 35}
+func (c Circle) Resized(radiusDelta float64) Circle {
+	return Circle{
+		Center: c.Center,
+		Radius: c.Radius + radiusDelta,
+	}
+}
+
+// Contains checks whether a vector `u` is contained within this Circle (including it's perimeter).
+func (c Circle) Contains(u Vec) bool {
+	toCenter := c.Center.To(u)
+	return c.Radius >= toCenter.Len()
+}
+
+// Formula returns the values of h and k, for the equation of the circle: (x-h)^2 + (y-k)^2 = r^2
+// where r is the radius of the circle.
+func (c Circle) Formula() (h, k float64) {
+	return c.Center.X, c.Center.Y
+}
+
+// maxCircle will return the larger circle based on the radius.
+func maxCircle(c, d Circle) Circle {
+	if c.Radius < d.Radius {
+		return d
+	}
+	return c
+}
+
+// minCircle will return the smaller circle based on the radius.
+func minCircle(c, d Circle) Circle {
+	if c.Radius < d.Radius {
+		return c
+	}
+	return d
+}
+
+// Union returns the minimal Circle which covers both `c` and `d`.
+func (c Circle) Union(d Circle) Circle {
+	biggerC := maxCircle(c.Norm(), d.Norm())
+	smallerC := minCircle(c.Norm(), d.Norm())
+
+	// Get distance between centers
+	dist := c.Center.To(d.Center).Len()
+
+	// If the bigger Circle encompasses the smaller one, we have the result
+	if dist+smallerC.Radius <= biggerC.Radius {
+		return biggerC
+	}
+
+	// Calculate radius for encompassing Circle
+	r := (dist + biggerC.Radius + smallerC.Radius) / 2
+
+	// Calculate center for encompassing Circle
+	theta := .5 + (biggerC.Radius-smallerC.Radius)/(2*dist)
+	center := Lerp(smallerC.Center, biggerC.Center, theta)
+
+	return Circle{
+		Center: center,
+		Radius: r,
+	}
+}
+
+// Intersect returns the maximal Circle which is covered by both `c` and `d`.
+//
+// If `c` and `d` don't overlap, this function returns a zero-sized circle at the centerpoint between the two Circle's
+// centers.
+func (c Circle) Intersect(d Circle) Circle {
+	// Check if one of the circles encompasses the other; if so, return that one
+	biggerC := maxCircle(c.Norm(), d.Norm())
+	smallerC := minCircle(c.Norm(), d.Norm())
+
+	if biggerC.Radius >= biggerC.Center.To(smallerC.Center).Len()+smallerC.Radius {
+		return biggerC
+	}
+
+	// Calculate the midpoint between the two radii
+	// Distance between centers
+	dist := c.Center.To(d.Center).Len()
+	// Difference between radii
+	diff := dist - (c.Radius + d.Radius)
+	// Distance from c.Center to the weighted midpoint
+	distToMidpoint := c.Radius + 0.5*diff
+	// Weighted midpoint
+	center := Lerp(c.Center, d.Center, distToMidpoint/dist)
+
+	// No need to calculate radius if the circles do not overlap
+	if c.Center.To(d.Center).Len() >= c.Radius+d.Radius {
+		return C(center, 0)
+	}
+
+	radius := c.Center.To(d.Center).Len() - (c.Radius + d.Radius)
+
+	return Circle{
+		Center: center,
+		Radius: math.Abs(radius),
+	}
+}
+
+// IntersectLine will return the shortest Vec such that if the Circle is moved by the Vec returned, the Line and Rect no
+// longer intersect.
+func (c Circle) IntersectLine(l Line) Vec {
+	return l.IntersectCircle(c).Scaled(-1)
+}
+
+// IntersectRect returns a minimal required Vector, such that moving the circle by that vector would stop the Circle
+// and the Rect intersecting.  This function returns a zero-vector if the Circle and Rect do not overlap, and if only
+// the perimeters touch.
+//
+// This function will return a non-zero vector if:
+//  - The Rect contains the Circle, partially or fully
+//  - The Circle contains the Rect, partially of fully
+func (c Circle) IntersectRect(r Rect) Vec {
+	// Checks if the c.Center is not in the diagonal quadrants of the rectangle
+	if (r.Min.X <= c.Center.X && c.Center.X <= r.Max.X) || (r.Min.Y <= c.Center.Y && c.Center.Y <= r.Max.Y) {
+		// 'grow' the Rect by c.Radius in each orthagonal
+		grown := Rect{Min: r.Min.Sub(V(c.Radius, c.Radius)), Max: r.Max.Add(V(c.Radius, c.Radius))}
+		if !grown.Contains(c.Center) {
+			// c.Center not close enough to overlap, return zero-vector
+			return ZV
+		}
+
+		// Get minimum distance to travel out of Rect
+		rToC := r.Center().To(c.Center)
+		h := c.Radius - math.Abs(rToC.X) + (r.W() / 2)
+		v := c.Radius - math.Abs(rToC.Y) + (r.H() / 2)
+
+		if rToC.X < 0 {
+			h = -h
+		}
+		if rToC.Y < 0 {
+			v = -v
+		}
+
+		// No intersect
+		if h == 0 && v == 0 {
+			return ZV
+		}
+
+		if math.Abs(h) > math.Abs(v) {
+			// Vertical distance shorter
+			return V(0, v)
+		}
+		return V(h, 0)
+	} else {
+		// The center is in the diagonal quadrants
+
+		// Helper points to make code below easy to read.
+		rectTopLeft := V(r.Min.X, r.Max.Y)
+		rectBottomRight := V(r.Max.X, r.Min.Y)
+
+		// Check for overlap.
+		if !(c.Contains(r.Min) || c.Contains(r.Max) || c.Contains(rectTopLeft) || c.Contains(rectBottomRight)) {
+			// No overlap.
+			return ZV
+		}
+
+		var centerToCorner Vec
+		if c.Center.To(r.Min).Len() <= c.Radius {
+			// Closest to bottom-left
+			centerToCorner = c.Center.To(r.Min)
+		}
+		if c.Center.To(r.Max).Len() <= c.Radius {
+			// Closest to top-right
+			centerToCorner = c.Center.To(r.Max)
+		}
+		if c.Center.To(rectTopLeft).Len() <= c.Radius {
+			// Closest to top-left
+			centerToCorner = c.Center.To(rectTopLeft)
+		}
+		if c.Center.To(rectBottomRight).Len() <= c.Radius {
+			// Closest to bottom-right
+			centerToCorner = c.Center.To(rectBottomRight)
+		}
+
+		cornerToCircumferenceLen := c.Radius - centerToCorner.Len()
+
+		return centerToCorner.Unit().Scaled(cornerToCircumferenceLen)
+	}
+}
+
+// IntersectionPoints returns all the points where the Circle intersects with the line provided.  This can be zero, one or
+// two points, depending on the location of the shapes.  The points of intersection will be returned in order of
+// closest-to-l.A to closest-to-l.B.
+func (c Circle) IntersectionPoints(l Line) []Vec {
+	cContainsA := c.Contains(l.A)
+	cContainsB := c.Contains(l.B)
+
+	// Special case for both endpoint being contained within the circle
+	if cContainsA && cContainsB {
+		return []Vec{}
+	}
+
+	// Get closest point on the line to this circles' center
+	closestToCenter := l.Closest(c.Center)
+
+	// If the distance to the closest point is greater than the radius, there are no points of intersection
+	if closestToCenter.To(c.Center).Len() > c.Radius {
+		return []Vec{}
+	}
+
+	// If the distance to the closest point is equal to the radius, the line is tangent and the closest point is the
+	// point at which it touches the circle.
+	if closestToCenter.To(c.Center).Len() == c.Radius {
+		return []Vec{closestToCenter}
+	}
+
+	// Special case for endpoint being on the circles' center
+	if c.Center == l.A || c.Center == l.B {
+		otherEnd := l.B
+		if c.Center == l.B {
+			otherEnd = l.A
+		}
+		intersect := c.Center.Add(c.Center.To(otherEnd).Unit().Scaled(c.Radius))
+		return []Vec{intersect}
+	}
+
+	// This means the distance to the closest point is less than the radius, so there is at least one intersection,
+	// possibly two.
+
+	// If one of the end points exists within the circle, there is only one intersection
+	if cContainsA || cContainsB {
+		containedPoint := l.A
+		otherEnd := l.B
+		if cContainsB {
+			containedPoint = l.B
+			otherEnd = l.A
+		}
+
+		// Use trigonometry to get the length of the line between the contained point and the intersection point.
+		// The following is used to describe the triangle formed:
+		//  - a is the side between contained point and circle center
+		//  - b is the side between the center and the intersection point (radius)
+		//  - c is the side between the contained point and the intersection point
+		// The captials of these letters are used as the angles opposite the respective sides.
+		// a and b are known
+		a := containedPoint.To(c.Center).Len()
+		b := c.Radius
+		// B can be calculated by subtracting the angle of b (to the x-axis) from the angle of c (to the x-axis)
+		B := containedPoint.To(c.Center).Angle() - containedPoint.To(otherEnd).Angle()
+		// Using the Sin rule we can get A
+		A := math.Asin((a * math.Sin(B)) / b)
+		// Using the rule that there are 180 degrees (or Pi radians) in a triangle, we can now get C
+		C := math.Pi - A + B
+		// If C is zero, the line segment is in-line with the center-intersect line.
+		var c float64
+		if C == 0 {
+			c = b - a
+		} else {
+			// Using the Sine rule again, we can now get c
+			c = (a * math.Sin(C)) / math.Sin(A)
+		}
+		// Travelling from the contained point to the other end by length of a will provide the intersection point.
+		return []Vec{
+			containedPoint.Add(containedPoint.To(otherEnd).Unit().Scaled(c)),
+		}
+	}
+
+	// Otherwise the endpoints exist outside of the circle, and the line segment intersects in two locations.
+	// The vector formed by going from the closest point to the center of the circle will be perpendicular to the line;
+	// this forms a right-angled triangle with the intersection points, with the radius as the hypotenuse.
+	// Calculate the other triangles' sides' length.
+	a := math.Sqrt(math.Pow(c.Radius, 2) - math.Pow(closestToCenter.To(c.Center).Len(), 2))
+
+	// Travelling in both directions from the closest point by length of a will provide the two intersection points.
+	first := closestToCenter.Add(closestToCenter.To(l.A).Unit().Scaled(a))
+	second := closestToCenter.Add(closestToCenter.To(l.B).Unit().Scaled(a))
+
+	if first.To(l.A).Len() < second.To(l.A).Len() {
+		return []Vec{first, second}
+	}
+	return []Vec{second, first}
+}