Merge pull request #157 from bcvery1/addcircle

Added circle geometry - small feature/improvement
This commit is contained in:
Michal Štrba 2019-02-14 16:00:46 +01:00 committed by GitHub
commit 8563c28493
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2 changed files with 754 additions and 7 deletions

View File

@ -318,6 +318,239 @@ func (r Rect) Intersect(s Rect) Rect {
return t
}
// IntersectCircle 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 (r Rect) IntersectCircle(c Circle) Vec {
return c.IntersectRect(r).Scaled(-1)
}
// 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()
}
// 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),
}
}
// 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 {
// h and v will hold the minimum horizontal and vertical distances (respectively) to avoid overlapping
var h, v float64
// 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
}
} else {
// The center is in the diagonal quadrants
if c.Center.To(r.Min).Len() <= c.Radius {
// Closest to bottom-left
cornerToCenter := r.Min.To(c.Center)
// Get the horizontal and vertical overlaps
h = c.Radius - math.Sqrt(math.Pow(c.Radius, 2)-math.Pow(cornerToCenter.Y, 2))
v = -1 * (c.Radius + math.Sqrt(math.Pow(c.Radius, 2)-math.Pow(cornerToCenter.X, 2)))
}
if c.Center.To(r.Max).Len() <= c.Radius {
// Closest to top-right
cornerToCenter := r.Max.To(c.Center)
// Get the horizontal and vertical overlaps
h = c.Radius - math.Sqrt(math.Pow(c.Radius, 2)-math.Pow(cornerToCenter.Y, 2))
v = c.Radius - math.Sqrt(math.Pow(c.Radius, 2)-math.Pow(cornerToCenter.X, 2))
}
if c.Center.To(V(r.Min.X, r.Max.Y)).Len() <= c.Radius {
// Closest to top-left
cornerToCenter := V(r.Min.X, r.Max.Y).To(c.Center)
// Get the horizontal and vertical overlaps
h = -1 * (c.Radius + math.Sqrt(math.Pow(c.Radius, 2)-math.Pow(cornerToCenter.Y, 2)))
v = c.Radius - math.Sqrt(math.Pow(c.Radius, 2)-math.Pow(cornerToCenter.X, 2))
}
if c.Center.To(V(r.Max.X, r.Min.Y)).Len() <= c.Radius {
// Closest to bottom-right
cornerToCenter := V(r.Max.X, r.Min.Y).To(c.Center)
// Get the horizontal and vertical overlaps
h = -1 * (c.Radius + math.Sqrt(math.Pow(c.Radius, 2)-math.Pow(cornerToCenter.Y, 2)))
v = -1 * (c.Radius + math.Sqrt(math.Pow(c.Radius, 2)-math.Pow(cornerToCenter.X, 2)))
}
}
// 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)
}
// Matrix is a 2x3 affine matrix that can be used for all kinds of spatial transforms, such
// as movement, scaling and rotations.
//

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@ -2,19 +2,19 @@ package pixel_test
import (
"fmt"
"github.com/stretchr/testify/assert"
"math"
"reflect"
"testing"
"github.com/faiface/pixel"
"github.com/stretchr/testify/assert"
)
type rectTestTransform struct {
name string
f func(pixel.Rect) pixel.Rect
}
func TestResizeRect(t *testing.T) {
func TestRect_Resize(t *testing.T) {
type rectTestTransform struct {
name string
f func(pixel.Rect) pixel.Rect
}
// rectangles
squareAroundOrigin := pixel.R(-10, -10, 10, 10)
@ -162,3 +162,517 @@ func TestMatrix_Unproject(t *testing.T) {
assert.True(t, math.IsNaN(unprojected.Y))
})
}
func TestC(t *testing.T) {
type args struct {
radius float64
center pixel.Vec
}
tests := []struct {
name string
args args
want pixel.Circle
}{
{
name: "C(): positive radius",
args: args{radius: 10, center: pixel.ZV},
want: pixel.Circle{Radius: 10, Center: pixel.ZV},
},
{
name: "C(): zero radius",
args: args{radius: 0, center: pixel.ZV},
want: pixel.Circle{Radius: 0, Center: pixel.ZV},
},
{
name: "C(): negative radius",
args: args{radius: -5, center: pixel.ZV},
want: pixel.Circle{Radius: -5, Center: pixel.ZV},
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
if got := pixel.C(tt.args.center, tt.args.radius); !reflect.DeepEqual(got, tt.want) {
t.Errorf("C() = %v, want %v", got, tt.want)
}
})
}
}
func TestCircle_String(t *testing.T) {
type fields struct {
radius float64
center pixel.Vec
}
tests := []struct {
name string
fields fields
want string
}{
{
name: "Circle.String(): positive radius",
fields: fields{radius: 10, center: pixel.ZV},
want: "Circle(Vec(0, 0), 10.00)",
},
{
name: "Circle.String(): zero radius",
fields: fields{radius: 0, center: pixel.ZV},
want: "Circle(Vec(0, 0), 0.00)",
},
{
name: "Circle.String(): negative radius",
fields: fields{radius: -5, center: pixel.ZV},
want: "Circle(Vec(0, 0), -5.00)",
},
{
name: "Circle.String(): irrational radius",
fields: fields{radius: math.Pi, center: pixel.ZV},
want: "Circle(Vec(0, 0), 3.14)",
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
c := pixel.C(tt.fields.center, tt.fields.radius)
if got := c.String(); got != tt.want {
t.Errorf("Circle.String() = %v, want %v", got, tt.want)
}
})
}
}
func TestCircle_Norm(t *testing.T) {
type fields struct {
radius float64
center pixel.Vec
}
tests := []struct {
name string
fields fields
want pixel.Circle
}{
{
name: "Circle.Norm(): positive radius",
fields: fields{radius: 10, center: pixel.ZV},
want: pixel.C(pixel.ZV, 10),
},
{
name: "Circle.Norm(): zero radius",
fields: fields{radius: 0, center: pixel.ZV},
want: pixel.C(pixel.ZV, 0),
},
{
name: "Circle.Norm(): negative radius",
fields: fields{radius: -5, center: pixel.ZV},
want: pixel.C(pixel.ZV, 5),
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
c := pixel.C(tt.fields.center, tt.fields.radius)
if got := c.Norm(); !reflect.DeepEqual(got, tt.want) {
t.Errorf("Circle.Norm() = %v, want %v", got, tt.want)
}
})
}
}
func TestCircle_Area(t *testing.T) {
type fields struct {
radius float64
center pixel.Vec
}
tests := []struct {
name string
fields fields
want float64
}{
{
name: "Circle.Area(): positive radius",
fields: fields{radius: 10, center: pixel.ZV},
want: 100 * math.Pi,
},
{
name: "Circle.Area(): zero radius",
fields: fields{radius: 0, center: pixel.ZV},
want: 0,
},
{
name: "Circle.Area(): negative radius",
fields: fields{radius: -5, center: pixel.ZV},
want: 25 * math.Pi,
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
c := pixel.C(tt.fields.center, tt.fields.radius)
if got := c.Area(); got != tt.want {
t.Errorf("Circle.Area() = %v, want %v", got, tt.want)
}
})
}
}
func TestCircle_Moved(t *testing.T) {
type fields struct {
radius float64
center pixel.Vec
}
type args struct {
delta pixel.Vec
}
tests := []struct {
name string
fields fields
args args
want pixel.Circle
}{
{
name: "Circle.Moved(): positive movement",
fields: fields{radius: 10, center: pixel.ZV},
args: args{delta: pixel.V(10, 20)},
want: pixel.C(pixel.V(10, 20), 10),
},
{
name: "Circle.Moved(): zero movement",
fields: fields{radius: 10, center: pixel.ZV},
args: args{delta: pixel.ZV},
want: pixel.C(pixel.V(0, 0), 10),
},
{
name: "Circle.Moved(): negative movement",
fields: fields{radius: 10, center: pixel.ZV},
args: args{delta: pixel.V(-5, -10)},
want: pixel.C(pixel.V(-5, -10), 10),
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
c := pixel.C(tt.fields.center, tt.fields.radius)
if got := c.Moved(tt.args.delta); !reflect.DeepEqual(got, tt.want) {
t.Errorf("Circle.Moved() = %v, want %v", got, tt.want)
}
})
}
}
func TestCircle_Resized(t *testing.T) {
type fields struct {
radius float64
center pixel.Vec
}
type args struct {
radiusDelta float64
}
tests := []struct {
name string
fields fields
args args
want pixel.Circle
}{
{
name: "Circle.Resized(): positive delta",
fields: fields{radius: 10, center: pixel.ZV},
args: args{radiusDelta: 5},
want: pixel.C(pixel.V(0, 0), 15),
},
{
name: "Circle.Resized(): zero delta",
fields: fields{radius: 10, center: pixel.ZV},
args: args{radiusDelta: 0},
want: pixel.C(pixel.V(0, 0), 10),
},
{
name: "Circle.Resized(): negative delta",
fields: fields{radius: 10, center: pixel.ZV},
args: args{radiusDelta: -5},
want: pixel.C(pixel.V(0, 0), 5),
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
c := pixel.C(tt.fields.center, tt.fields.radius)
if got := c.Resized(tt.args.radiusDelta); !reflect.DeepEqual(got, tt.want) {
t.Errorf("Circle.Resized() = %v, want %v", got, tt.want)
}
})
}
}
func TestCircle_Contains(t *testing.T) {
type fields struct {
radius float64
center pixel.Vec
}
type args struct {
u pixel.Vec
}
tests := []struct {
name string
fields fields
args args
want bool
}{
{
name: "Circle.Contains(): point on cicles' center",
fields: fields{radius: 10, center: pixel.ZV},
args: args{u: pixel.ZV},
want: true,
},
{
name: "Circle.Contains(): point offcenter",
fields: fields{radius: 10, center: pixel.V(5, 0)},
args: args{u: pixel.ZV},
want: true,
},
{
name: "Circle.Contains(): point on circumference",
fields: fields{radius: 10, center: pixel.V(10, 0)},
args: args{u: pixel.ZV},
want: true,
},
{
name: "Circle.Contains(): point outside circle",
fields: fields{radius: 10, center: pixel.V(15, 0)},
args: args{u: pixel.ZV},
want: false,
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
c := pixel.C(tt.fields.center, tt.fields.radius)
if got := c.Contains(tt.args.u); got != tt.want {
t.Errorf("Circle.Contains() = %v, want %v", got, tt.want)
}
})
}
}
func TestCircle_Union(t *testing.T) {
type fields struct {
radius float64
center pixel.Vec
}
type args struct {
d pixel.Circle
}
tests := []struct {
name string
fields fields
args args
want pixel.Circle
}{
{
name: "Circle.Union(): overlapping circles",
fields: fields{radius: 5, center: pixel.ZV},
args: args{d: pixel.C(pixel.ZV, 5)},
want: pixel.C(pixel.ZV, 5),
},
{
name: "Circle.Union(): separate circles",
fields: fields{radius: 1, center: pixel.ZV},
args: args{d: pixel.C(pixel.V(0, 2), 1)},
want: pixel.C(pixel.V(0, 1), 2),
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
c := pixel.C(tt.fields.center, tt.fields.radius)
if got := c.Union(tt.args.d); !reflect.DeepEqual(got, tt.want) {
t.Errorf("Circle.Union() = %v, want %v", got, tt.want)
}
})
}
}
func TestCircle_Intersect(t *testing.T) {
type fields struct {
radius float64
center pixel.Vec
}
type args struct {
d pixel.Circle
}
tests := []struct {
name string
fields fields
args args
want pixel.Circle
}{
{
name: "Circle.Intersect(): intersecting circles",
fields: fields{radius: 1, center: pixel.ZV},
args: args{d: pixel.C(pixel.V(1, 0), 1)},
want: pixel.C(pixel.V(0.5, 0), 1),
},
{
name: "Circle.Intersect(): non-intersecting circles",
fields: fields{radius: 1, center: pixel.ZV},
args: args{d: pixel.C(pixel.V(3, 3), 1)},
want: pixel.C(pixel.V(1.5, 1.5), 0),
},
{
name: "Circle.Intersect(): first circle encompassing second",
fields: fields{radius: 10, center: pixel.ZV},
args: args{d: pixel.C(pixel.V(3, 3), 1)},
want: pixel.C(pixel.ZV, 10),
},
{
name: "Circle.Intersect(): second circle encompassing first",
fields: fields{radius: 1, center: pixel.V(-1, -4)},
args: args{d: pixel.C(pixel.ZV, 10)},
want: pixel.C(pixel.ZV, 10),
},
{
name: "Circle.Intersect(): matching circles",
fields: fields{radius: 1, center: pixel.ZV},
args: args{d: pixel.C(pixel.ZV, 1)},
want: pixel.C(pixel.ZV, 1),
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
c := pixel.C(
tt.fields.center,
tt.fields.radius,
)
if got := c.Intersect(tt.args.d); !reflect.DeepEqual(got, tt.want) {
t.Errorf("Circle.Intersect() = %v, want %v", got, tt.want)
}
})
}
}
func TestRect_IntersectCircle(t *testing.T) {
type fields struct {
Min pixel.Vec
Max pixel.Vec
}
type args struct {
c pixel.Circle
}
tests := []struct {
name string
fields fields
args args
want pixel.Vec
}{
{
name: "Rect.IntersectCircle(): no overlap",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(50, 50), 1)},
want: pixel.ZV,
},
{
name: "Rect.IntersectCircle(): circle contains rect",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(5, 5), 10)},
want: pixel.V(-15, 0),
},
{
name: "Rect.IntersectCircle(): rect contains circle",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(5, 5), 1)},
want: pixel.V(-6, 0),
},
{
name: "Rect.IntersectCircle(): circle overlaps bottom-left corner",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(0, 0), 1)},
want: pixel.V(1, 0),
},
{
name: "Rect.IntersectCircle(): circle overlaps top-left corner",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(0, 10), 1)},
want: pixel.V(1, 0),
},
{
name: "Rect.IntersectCircle(): circle overlaps bottom-right corner",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(10, 0), 1)},
want: pixel.V(-1, 0),
},
{
name: "Rect.IntersectCircle(): circle overlaps top-right corner",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(10, 10), 1)},
want: pixel.V(-1, 0),
},
{
name: "Rect.IntersectCircle(): circle overlaps two corners",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(0, 5), 6)},
want: pixel.V(6, 0),
},
{
name: "Rect.IntersectCircle(): circle overlaps left edge",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(0, 5), 1)},
want: pixel.V(1, 0),
},
{
name: "Rect.IntersectCircle(): circle overlaps bottom edge",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(5, 0), 1)},
want: pixel.V(0, 1),
},
{
name: "Rect.IntersectCircle(): circle overlaps right edge",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(10, 5), 1)},
want: pixel.V(-1, 0),
},
{
name: "Rect.IntersectCircle(): circle overlaps top edge",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(5, 10), 1)},
want: pixel.V(0, -1),
},
{
name: "Rect.IntersectCircle(): edge is tangent of left side",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(-1, 5), 1)},
want: pixel.ZV,
},
{
name: "Rect.IntersectCircle(): edge is tangent of top side",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(5, -1), 1)},
want: pixel.ZV,
},
{
name: "Rect.IntersectCircle(): circle above rectangle",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(5, 12), 1)},
want: pixel.ZV,
},
{
name: "Rect.IntersectCircle(): circle below rectangle",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(5, -2), 1)},
want: pixel.ZV,
},
{
name: "Rect.IntersectCircle(): circle left of rectangle",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(-1, 5), 1)},
want: pixel.ZV,
},
{
name: "Rect.IntersectCircle(): circle right of rectangle",
fields: fields{Min: pixel.ZV, Max: pixel.V(10, 10)},
args: args{c: pixel.C(pixel.V(11, 5), 1)},
want: pixel.ZV,
},
}
for _, tt := range tests {
t.Run(tt.name, func(t *testing.T) {
r := pixel.Rect{
Min: tt.fields.Min,
Max: tt.fields.Max,
}
if got := r.IntersectCircle(tt.args.c); got != tt.want {
t.Errorf("Rect.IntersectCircle() = %v, want %v", got, tt.want)
}
})
}
}