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actually add the files -.-

This commit is contained in:
Anten Skrabec 2021-06-22 14:45:22 -06:00
parent 7fe32e1553
commit 4a8b06746f
5 changed files with 1188 additions and 0 deletions
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334
circle.go Normal file
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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}
}

15
math.go Normal file
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package pixel
// Clamp returns x clamped to the interval [min, max].
//
// If x is less than min, min is returned. If x is more than max, max is returned. Otherwise, x is
// returned.
func Clamp(x, min, max float64) float64 {
if x < min {
return min
}
if x > max {
return max
}
return x
}

98
matrix.go Normal file
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package pixel
import (
"fmt"
"math"
)
// Matrix is a 2x3 affine matrix that can be used for all kinds of spatial transforms, such
// as movement, scaling and rotations.
//
// Matrix has a handful of useful methods, each of which adds a transformation to the matrix. For
// example:
//
// pixel.IM.Moved(pixel.V(100, 200)).Rotated(pixel.ZV, math.Pi/2)
//
// This code creates a Matrix that first moves everything by 100 units horizontally and 200 units
// vertically and then rotates everything by 90 degrees around the origin.
//
// Layout is:
// [0] [2] [4]
// [1] [3] [5]
// 0 0 1 (implicit row)
type Matrix [6]float64
// IM stands for identity matrix. Does nothing, no transformation.
var IM = Matrix{1, 0, 0, 1, 0, 0}
// String returns a string representation of the Matrix.
//
// m := pixel.IM
// fmt.Println(m) // Matrix(1 0 0 | 0 1 0)
func (m Matrix) String() string {
return fmt.Sprintf(
"Matrix(%v %v %v | %v %v %v)",
m[0], m[2], m[4],
m[1], m[3], m[5],
)
}
// Moved moves everything by the delta vector.
func (m Matrix) Moved(delta Vec) Matrix {
m[4], m[5] = m[4]+delta.X, m[5]+delta.Y
return m
}
// ScaledXY scales everything around a given point by the scale factor in each axis respectively.
func (m Matrix) ScaledXY(around Vec, scale Vec) Matrix {
m[4], m[5] = m[4]-around.X, m[5]-around.Y
m[0], m[2], m[4] = m[0]*scale.X, m[2]*scale.X, m[4]*scale.X
m[1], m[3], m[5] = m[1]*scale.Y, m[3]*scale.Y, m[5]*scale.Y
m[4], m[5] = m[4]+around.X, m[5]+around.Y
return m
}
// Scaled scales everything around a given point by the scale factor.
func (m Matrix) Scaled(around Vec, scale float64) Matrix {
return m.ScaledXY(around, V(scale, scale))
}
// Rotated rotates everything around a given point by the given angle in radians.
func (m Matrix) Rotated(around Vec, angle float64) Matrix {
sint, cost := math.Sincos(angle)
m[4], m[5] = m[4]-around.X, m[5]-around.Y
m = m.Chained(Matrix{cost, sint, -sint, cost, 0, 0})
m[4], m[5] = m[4]+around.X, m[5]+around.Y
return m
}
// Chained adds another Matrix to this one. All tranformations by the next Matrix will be applied
// after the transformations of this Matrix.
func (m Matrix) Chained(next Matrix) Matrix {
return Matrix{
next[0]*m[0] + next[2]*m[1],
next[1]*m[0] + next[3]*m[1],
next[0]*m[2] + next[2]*m[3],
next[1]*m[2] + next[3]*m[3],
next[0]*m[4] + next[2]*m[5] + next[4],
next[1]*m[4] + next[3]*m[5] + next[5],
}
}
// Project applies all transformations added to the Matrix to a vector u and returns the result.
//
// Time complexity is O(1).
func (m Matrix) Project(u Vec) Vec {
return Vec{m[0]*u.X + m[2]*u.Y + m[4], m[1]*u.X + m[3]*u.Y + m[5]}
}
// Unproject does the inverse operation to Project.
//
// Time complexity is O(1).
func (m Matrix) Unproject(u Vec) Vec {
det := m[0]*m[3] - m[2]*m[1]
return Vec{
(m[3]*(u.X-m[4]) - m[2]*(u.Y-m[5])) / det,
(-m[1]*(u.X-m[4]) + m[0]*(u.Y-m[5])) / det,
}
}

284
rectangle.go Normal file
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package pixel
import (
"fmt"
"math"
)
// Rect is a 2D rectangle aligned with the axes of the coordinate system. It is defined by two
// points, Min and Max.
//
// The invariant should hold, that Max's components are greater or equal than Min's components
// respectively.
type Rect struct {
Min, Max Vec
}
// ZR is a zero rectangle.
var ZR = Rect{Min: ZV, Max: ZV}
// R returns a new Rect with given the Min and Max coordinates.
//
// Note that the returned rectangle is not automatically normalized.
func R(minX, minY, maxX, maxY float64) Rect {
return Rect{
Min: Vec{minX, minY},
Max: Vec{maxX, maxY},
}
}
// String returns the string representation of the Rect.
//
// r := pixel.R(100, 50, 200, 300)
// r.String() // returns "Rect(100, 50, 200, 300)"
// fmt.Println(r) // Rect(100, 50, 200, 300)
func (r Rect) String() string {
return fmt.Sprintf("Rect(%v, %v, %v, %v)", r.Min.X, r.Min.Y, r.Max.X, r.Max.Y)
}
// Norm returns the Rect in normal form, such that Max is component-wise greater or equal than Min.
func (r Rect) Norm() Rect {
return Rect{
Min: Vec{
math.Min(r.Min.X, r.Max.X),
math.Min(r.Min.Y, r.Max.Y),
},
Max: Vec{
math.Max(r.Min.X, r.Max.X),
math.Max(r.Min.Y, r.Max.Y),
},
}
}
// W returns the width of the Rect.
func (r Rect) W() float64 {
return r.Max.X - r.Min.X
}
// H returns the height of the Rect.
func (r Rect) H() float64 {
return r.Max.Y - r.Min.Y
}
// Size returns the vector of width and height of the Rect.
func (r Rect) Size() Vec {
return V(r.W(), r.H())
}
// Area returns the area of r. If r is not normalized, area may be negative.
func (r Rect) Area() float64 {
return r.W() * r.H()
}
// Edges will return the four lines which make up the edges of the rectangle.
func (r Rect) Edges() [4]Line {
corners := r.Vertices()
return [4]Line{
{A: corners[0], B: corners[1]},
{A: corners[1], B: corners[2]},
{A: corners[2], B: corners[3]},
{A: corners[3], B: corners[0]},
}
}
// Anchor is a vector used to define anchors, such as `Center`, `Top`, `TopRight`, etc.
type Anchor Vec
var (
Center = Anchor{0.5, 0.5}
Top = Anchor{0.5, 0}
TopRight = Anchor{0, 0}
Right = Anchor{0, 0.5}
BottomRight = Anchor{0, 1}
Bottom = Anchor{0.5, 1}
BottomLeft = Anchor{1, 1}
Left = Anchor{1, 0.5}
TopLeft = Anchor{1, 0}
)
var anchorStrings map[Anchor]string = map[Anchor]string{
Center: "center",
Top: "top",
TopRight: "top-right",
Right: "right",
BottomRight: "bottom-right",
Bottom: "bottom",
BottomLeft: "bottom-left",
Left: "left",
TopLeft: "top-left",
}
// String returns the string representation of an anchor.
func (anchor Anchor) String() string {
return anchorStrings[anchor]
}
var oppositeAnchors map[Anchor]Anchor = map[Anchor]Anchor{
Center: Center,
Top: Bottom,
Bottom: Top,
Right: Left,
Left: Right,
TopRight: BottomLeft,
BottomLeft: TopRight,
BottomRight: TopLeft,
TopLeft: BottomRight,
}
// Opposite returns the opposite position of the anchor (ie. Top -> Bottom; BottomLeft -> TopRight, etc.).
func (anchor Anchor) Opposite() Anchor {
return oppositeAnchors[anchor]
}
// AnchorPos returns the relative position of the given anchor.
func (r Rect) AnchorPos(anchor Anchor) Vec {
return r.Size().ScaledXY(V(0, 0).Sub(Vec(anchor)))
}
// AlignedTo returns the rect moved by the given anchor.
func (rect Rect) AlignedTo(anchor Anchor) Rect {
return rect.Moved(rect.AnchorPos(anchor))
}
// Center returns the position of the center of the Rect.
// `rect.Center()` is equivalent to `rect.Anchor(pixel.Anchor.Center)`
func (r Rect) Center() Vec {
return Lerp(r.Min, r.Max, 0.5)
}
// Moved returns the Rect moved (both Min and Max) by the given vector delta.
func (r Rect) Moved(delta Vec) Rect {
return Rect{
Min: r.Min.Add(delta),
Max: r.Max.Add(delta),
}
}
// Resized returns the Rect resized to the given size while keeping the position of the given
// anchor.
//
// r.Resized(r.Min, size) // resizes while keeping the position of the lower-left corner
// r.Resized(r.Max, size) // same with the top-right corner
// r.Resized(r.Center(), size) // resizes around the center
//
// This function does not make sense for resizing a rectangle of zero area and will panic. Use
// ResizedMin in the case of zero area.
func (r Rect) Resized(anchor, size Vec) Rect {
if r.W()*r.H() == 0 {
panic(fmt.Errorf("(%T).Resize: zero area", r))
}
fraction := Vec{size.X / r.W(), size.Y / r.H()}
return Rect{
Min: anchor.Add(r.Min.Sub(anchor).ScaledXY(fraction)),
Max: anchor.Add(r.Max.Sub(anchor).ScaledXY(fraction)),
}
}
// ResizedMin returns the Rect resized to the given size while keeping the position of the Rect's
// Min.
//
// Sizes of zero area are safe here.
func (r Rect) ResizedMin(size Vec) Rect {
return Rect{
Min: r.Min,
Max: r.Min.Add(size),
}
}
// Contains checks whether a vector u is contained within this Rect (including it's borders).
func (r Rect) Contains(u Vec) bool {
return r.Min.X <= u.X && u.X <= r.Max.X && r.Min.Y <= u.Y && u.Y <= r.Max.Y
}
// Union returns the minimal Rect which covers both r and s. Rects r and s must be normalized.
func (r Rect) Union(s Rect) Rect {
return R(
math.Min(r.Min.X, s.Min.X),
math.Min(r.Min.Y, s.Min.Y),
math.Max(r.Max.X, s.Max.X),
math.Max(r.Max.Y, s.Max.Y),
)
}
// Intersect returns the maximal Rect which is covered by both r and s. Rects r and s must be normalized.
//
// If r and s don't overlap, this function returns a zero-rectangle.
func (r Rect) Intersect(s Rect) Rect {
t := R(
math.Max(r.Min.X, s.Min.X),
math.Max(r.Min.Y, s.Min.Y),
math.Min(r.Max.X, s.Max.X),
math.Min(r.Max.Y, s.Max.Y),
)
if t.Min.X >= t.Max.X || t.Min.Y >= t.Max.Y {
return ZR
}
return t
}
// Intersects returns whether or not the given Rect intersects at any point with this Rect.
//
// This function is overall about 5x faster than Intersect, so it is better
// to use if you have no need for the returned Rect from Intersect.
func (r Rect) Intersects(s Rect) bool {
return !(s.Max.X < r.Min.X ||
s.Min.X > r.Max.X ||
s.Max.Y < r.Min.Y ||
s.Min.Y > r.Max.Y)
}
// IntersectCircle returns a minimal required Vector, such that moving the rect 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)
}
// IntersectLine will return the shortest Vec such that if the Rect is moved by the Vec returned, the Line and Rect no
// longer intersect.
func (r Rect) IntersectLine(l Line) Vec {
return l.IntersectRect(r).Scaled(-1)
}
// IntersectionPoints returns all the points where the Rect 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 (r Rect) IntersectionPoints(l Line) []Vec {
// Use map keys to ensure unique points
pointMap := make(map[Vec]struct{})
for _, edge := range r.Edges() {
if intersect, ok := l.Intersect(edge); ok {
pointMap[intersect] = struct{}{}
}
}
points := make([]Vec, 0, len(pointMap))
for point := range pointMap {
points = append(points, point)
}
// Order the points
if len(points) == 2 {
if points[1].To(l.A).Len() < points[0].To(l.A).Len() {
return []Vec{points[1], points[0]}
}
}
return points
}
// Vertices returns a slice of the four corners which make up the rectangle.
func (r Rect) Vertices() [4]Vec {
return [4]Vec{
r.Min,
V(r.Min.X, r.Max.Y),
r.Max,
V(r.Max.X, r.Min.Y),
}
}

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vector.go Normal file
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package pixel
import (
"fmt"
"math"
)
// Vec is a 2D vector type with X and Y coordinates.
//
// Create vectors with the V constructor:
//
// u := pixel.V(1, 2)
// v := pixel.V(8, -3)
//
// Use various methods to manipulate them:
//
// w := u.Add(v)
// fmt.Println(w) // Vec(9, -1)
// fmt.Println(u.Sub(v)) // Vec(-7, 5)
// u = pixel.V(2, 3)
// v = pixel.V(8, 1)
// if u.X < 0 {
// fmt.Println("this won't happen")
// }
// x := u.Unit().Dot(v.Unit())
type Vec struct {
X, Y float64
}
// ZV is a zero vector.
var ZV = Vec{0, 0}
// V returns a new 2D vector with the given coordinates.
func V(x, y float64) Vec {
return Vec{x, y}
}
// nearlyEqual compares two float64s and returns whether they are equal, accounting for rounding errors.At worst, the
// result is correct to 7 significant digits.
func nearlyEqual(a, b float64) bool {
epsilon := 0.000001
if a == b {
return true
}
diff := math.Abs(a - b)
if a == 0.0 || b == 0.0 || diff < math.SmallestNonzeroFloat64 {
return diff < (epsilon * math.SmallestNonzeroFloat64)
}
absA := math.Abs(a)
absB := math.Abs(b)
return diff/math.Min(absA+absB, math.MaxFloat64) < epsilon
}
// Eq will compare two vectors and return whether they are equal accounting for rounding errors. At worst, the result
// is correct to 7 significant digits.
func (u Vec) Eq(v Vec) bool {
return nearlyEqual(u.X, v.X) && nearlyEqual(u.Y, v.Y)
}
// Unit returns a vector of length 1 facing the given angle.
func Unit(angle float64) Vec {
return Vec{1, 0}.Rotated(angle)
}
// String returns the string representation of the vector u.
//
// u := pixel.V(4.5, -1.3)
// u.String() // returns "Vec(4.5, -1.3)"
// fmt.Println(u) // Vec(4.5, -1.3)
func (u Vec) String() string {
return fmt.Sprintf("Vec(%v, %v)", u.X, u.Y)
}
// XY returns the components of the vector in two return values.
func (u Vec) XY() (x, y float64) {
return u.X, u.Y
}
// Add returns the sum of vectors u and v.
func (u Vec) Add(v Vec) Vec {
return Vec{
u.X + v.X,
u.Y + v.Y,
}
}
// Sub returns the difference betweeen vectors u and v.
func (u Vec) Sub(v Vec) Vec {
return Vec{
u.X - v.X,
u.Y - v.Y,
}
}
// Floor converts x and y to their integer equivalents.
func (u Vec) Floor() Vec {
return Vec{
math.Floor(u.X),
math.Floor(u.Y),
}
}
// To returns the vector from u to v. Equivalent to v.Sub(u).
func (u Vec) To(v Vec) Vec {
return Vec{
v.X - u.X,
v.Y - u.Y,
}
}
// Scaled returns the vector u multiplied by c.
func (u Vec) Scaled(c float64) Vec {
return Vec{u.X * c, u.Y * c}
}
// ScaledXY returns the vector u multiplied by the vector v component-wise.
func (u Vec) ScaledXY(v Vec) Vec {
return Vec{u.X * v.X, u.Y * v.Y}
}
// Len returns the length of the vector u.
func (u Vec) Len() float64 {
return math.Hypot(u.X, u.Y)
}
// Angle returns the angle between the vector u and the x-axis. The result is in range [-Pi, Pi].
func (u Vec) Angle() float64 {
return math.Atan2(u.Y, u.X)
}
// Unit returns a vector of length 1 facing the direction of u (has the same angle).
func (u Vec) Unit() Vec {
if u.X == 0 && u.Y == 0 {
return Vec{1, 0}
}
return u.Scaled(1 / u.Len())
}
// Rotated returns the vector u rotated by the given angle in radians.
func (u Vec) Rotated(angle float64) Vec {
sin, cos := math.Sincos(angle)
return Vec{
u.X*cos - u.Y*sin,
u.X*sin + u.Y*cos,
}
}
// Normal returns a vector normal to u. Equivalent to u.Rotated(math.Pi / 2), but faster.
func (u Vec) Normal() Vec {
return Vec{-u.Y, u.X}
}
// Dot returns the dot product of vectors u and v.
func (u Vec) Dot(v Vec) float64 {
return u.X*v.X + u.Y*v.Y
}
// Cross return the cross product of vectors u and v.
func (u Vec) Cross(v Vec) float64 {
return u.X*v.Y - v.X*u.Y
}
// Project returns a projection (or component) of vector u in the direction of vector v.
//
// Behaviour is undefined if v is a zero vector.
func (u Vec) Project(v Vec) Vec {
len := u.Dot(v) / v.Len()
return v.Unit().Scaled(len)
}
// Map applies the function f to both x and y components of the vector u and returns the modified
// vector.
//
// u := pixel.V(10.5, -1.5)
// v := u.Map(math.Floor) // v is Vec(10, -2), both components of u floored
func (u Vec) Map(f func(float64) float64) Vec {
return Vec{
f(u.X),
f(u.Y),
}
}
// Lerp returns a linear interpolation between vectors a and b.
//
// This function basically returns a point along the line between a and b and t chooses which one.
// If t is 0, then a will be returned, if t is 1, b will be returned. Anything between 0 and 1 will
// return the appropriate point between a and b and so on.
func Lerp(a, b Vec, t float64) Vec {
return a.Scaled(1 - t).Add(b.Scaled(t))
}
// Line is a 2D line segment, between points A and B.
type Line struct {
A, B Vec
}
// L creates and returns a new Line.
func L(from, to Vec) Line {
return Line{
A: from,
B: to,
}
}
// Bounds returns the lines bounding box. This is in the form of a normalized Rect.
func (l Line) Bounds() Rect {
return R(l.A.X, l.A.Y, l.B.X, l.B.Y).Norm()
}
// Center will return the point at center of the line; that is, the point equidistant from either end.
func (l Line) Center() Vec {
return l.A.Add(l.A.To(l.B).Scaled(0.5))
}
// Closest will return the point on the line which is closest to the Vec provided.
func (l Line) Closest(v Vec) Vec {
// between is a helper function which determines whether x is greater than min(a, b) and less than max(a, b)
between := func(a, b, x float64) bool {
min := math.Min(a, b)
max := math.Max(a, b)
return min < x && x < max
}
// Closest point will be on a line which perpendicular to this line.
// If and only if the infinite perpendicular line intersects the segment.
m, b := l.Formula()
// Account for horizontal lines
if m == 0 {
x := v.X
y := l.A.Y
// check if the X coordinate of v is on the line
if between(l.A.X, l.B.X, v.X) {
return V(x, y)
}
// Otherwise get the closest endpoint
if l.A.To(v).Len() < l.B.To(v).Len() {
return l.A
}
return l.B
}
// Account for vertical lines
if math.IsInf(math.Abs(m), 1) {
x := l.A.X
y := v.Y
// check if the Y coordinate of v is on the line
if between(l.A.Y, l.B.Y, v.Y) {
return V(x, y)
}
// Otherwise get the closest endpoint
if l.A.To(v).Len() < l.B.To(v).Len() {
return l.A
}
return l.B
}
perpendicularM := -1 / m
perpendicularB := v.Y - (perpendicularM * v.X)
// Coordinates of intersect (of infinite lines)
x := (perpendicularB - b) / (m - perpendicularM)
y := m*x + b
// Check if the point lies between the x and y bounds of the segment
if !between(l.A.X, l.B.X, x) && !between(l.A.Y, l.B.Y, y) {
// Not within bounding box
toStart := v.To(l.A)
toEnd := v.To(l.B)
if toStart.Len() < toEnd.Len() {
return l.A
}
return l.B
}
return V(x, y)
}
// Contains returns whether the provided Vec lies on the line.
func (l Line) Contains(v Vec) bool {
return l.Closest(v).Eq(v)
}
// Formula will return the values that represent the line in the formula: y = mx + b
// This function will return math.Inf+, math.Inf- for a vertical line.
func (l Line) Formula() (m, b float64) {
// Account for horizontal lines
if l.B.Y == l.A.Y {
return 0, l.A.Y
}
m = (l.B.Y - l.A.Y) / (l.B.X - l.A.X)
b = l.A.Y - (m * l.A.X)
return m, b
}
// Intersect will return the point of intersection for the two line segments. If the line segments do not intersect,
// this function will return the zero-vector and false.
func (l Line) Intersect(k Line) (Vec, bool) {
// Check if the lines are parallel
lDir := l.A.To(l.B)
kDir := k.A.To(k.B)
if lDir.X == kDir.X && lDir.Y == kDir.Y {
return ZV, false
}
// The lines intersect - but potentially not within the line segments.
// Get the intersection point for the lines if they were infinitely long, check if the point exists on both of the
// segments
lm, lb := l.Formula()
km, kb := k.Formula()
// Account for vertical lines
if math.IsInf(math.Abs(lm), 1) && math.IsInf(math.Abs(km), 1) {
// Both vertical, therefore parallel
return ZV, false
}
var x, y float64
if math.IsInf(math.Abs(lm), 1) || math.IsInf(math.Abs(km), 1) {
// One line is vertical
intersectM := lm
intersectB := lb
verticalLine := k
if math.IsInf(math.Abs(lm), 1) {
intersectM = km
intersectB = kb
verticalLine = l
}
y = intersectM*verticalLine.A.X + intersectB
x = verticalLine.A.X
} else {
// Coordinates of intersect
x = (kb - lb) / (lm - km)
y = lm*x + lb
}
if l.Contains(V(x, y)) && k.Contains(V(x, y)) {
// The intersect point is on both line segments, they intersect.
return V(x, y), true
}
return ZV, false
}
// IntersectCircle will return the shortest Vec such that moving the Line by that Vec will cause the Line and Circle
// to no longer intesect. If they do not intersect at all, this function will return a zero-vector.
func (l Line) IntersectCircle(c Circle) Vec {
// Get the point on the line closest to the center of the circle.
closest := l.Closest(c.Center)
cirToClosest := c.Center.To(closest)
if cirToClosest.Len() >= c.Radius {
return ZV
}
return cirToClosest.Scaled(cirToClosest.Len() - c.Radius)
}
// IntersectRect will return the shortest Vec such that moving the Line by that Vec will cause the Line and Rect to
// no longer intesect. If they do not intersect at all, this function will return a zero-vector.
func (l Line) IntersectRect(r Rect) Vec {
// Check if either end of the line segment are within the rectangle
if r.Contains(l.A) || r.Contains(l.B) {
// Use the Rect.Intersect to get minimal return value
rIntersect := l.Bounds().Intersect(r)
if rIntersect.H() > rIntersect.W() {
// Go vertical
return V(0, rIntersect.H())
}
return V(rIntersect.W(), 0)
}
// Check if any of the rectangles' edges intersect with this line.
for _, edge := range r.Edges() {
if _, ok := l.Intersect(edge); ok {
// Get the closest points on the line to each corner, where:
// - the point is contained by the rectangle
// - the point is not the corner itself
corners := r.Vertices()
var closest *Vec
closestCorner := corners[0]
for _, c := range corners {
cc := l.Closest(c)
if closest == nil || (closest.Len() > cc.Len() && r.Contains(cc)) {
closest = &cc
closestCorner = c
}
}
return closest.To(closestCorner)
}
}
// No intersect
return ZV
}
// Len returns the length of the line segment.
func (l Line) Len() float64 {
return l.A.To(l.B).Len()
}
// Moved will return a line moved by the delta Vec provided.
func (l Line) Moved(delta Vec) Line {
return Line{
A: l.A.Add(delta),
B: l.B.Add(delta),
}
}
// Rotated will rotate the line around the provided Vec.
func (l Line) Rotated(around Vec, angle float64) Line {
// Move the line so we can use `Vec.Rotated`
lineShifted := l.Moved(around.Scaled(-1))
lineRotated := Line{
A: lineShifted.A.Rotated(angle),
B: lineShifted.B.Rotated(angle),
}
return lineRotated.Moved(around)
}
// Scaled will return the line scaled around the center point.
func (l Line) Scaled(scale float64) Line {
return l.ScaledXY(l.Center(), scale)
}
// ScaledXY will return the line scaled around the Vec provided.
func (l Line) ScaledXY(around Vec, scale float64) Line {
toA := around.To(l.A).Scaled(scale)
toB := around.To(l.B).Scaled(scale)
return Line{
A: around.Add(toA),
B: around.Add(toB),
}
}
func (l Line) String() string {
return fmt.Sprintf("Line(%v, %v)", l.A, l.B)
}