chore: Unify math types, utils and functions (#8389)

Co-authored-by: dwelle <5153846+dwelle@users.noreply.github.com>

packages/math/types.ts

@@ -0,0 +1,130 @@
+//
+// Measurements
+//
+
+/**
+ * By definition one radian is the angle subtended at the centre
+ * of a circle by an arc that is equal in length to the radius.
+ */
+export type Radians = number & { _brand: "excalimath__radian" };
+
+/**
+ * An angle measurement of a plane angle in which one full
+ * rotation is 360 degrees.
+ */
+export type Degrees = number & { _brand: "excalimath_degree" };
+
+//
+// Range
+//
+
+/**
+ * A number range which includes the start and end numbers in the range.
+ */
+export type InclusiveRange = [number, number] & { _brand: "excalimath_degree" };
+
+//
+// Point
+//
+
+/**
+ * Represents a 2D position in world or canvas space. A
+ * global coordinate.
+ */
+export type GlobalPoint = [x: number, y: number] & {
+  _brand: "excalimath__globalpoint";
+};
+
+/**
+ * Represents a 2D position in whatever local space it's
+ * needed. A local coordinate.
+ */
+export type LocalPoint = [x: number, y: number] & {
+  _brand: "excalimath__localpoint";
+};
+
+// Line
+
+/**
+ * A line is an infinitely long object with no width, depth, or curvature.
+ */
+export type Line<P extends GlobalPoint | LocalPoint> = [p: P, q: P] & {
+  _brand: "excalimath_line";
+};
+
+/**
+ * In geometry, a line segment is a part of a straight
+ * line that is bounded by two distinct end points, and
+ * contains every point on the line that is between its endpoints.
+ */
+export type LineSegment<P extends GlobalPoint | LocalPoint> = [a: P, b: P] & {
+  _brand: "excalimath_linesegment";
+};
+
+//
+// Vector
+//
+
+/**
+ * Represents a 2D vector
+ */
+export type Vector = [u: number, v: number] & {
+  _brand: "excalimath__vector";
+};
+
+// Triangles
+
+/**
+ * A triangle represented by 3 points
+ */
+export type Triangle<P extends GlobalPoint | LocalPoint> = [
+  a: P,
+  b: P,
+  c: P,
+] & {
+  _brand: "excalimath__triangle";
+};
+
+//
+// Polygon
+//
+
+/**
+ * A polygon is a closed shape by connecting the given points
+ * rectangles and diamonds are modelled by polygons
+ */
+export type Polygon<Point extends GlobalPoint | LocalPoint> = Point[] & {
+  _brand: "excalimath_polygon";
+};
+
+//
+// Curve
+//
+
+/**
+ * Cubic bezier curve with four control points
+ */
+export type Curve<Point extends GlobalPoint | LocalPoint> = [
+  Point,
+  Point,
+  Point,
+  Point,
+] & {
+  _brand: "excalimath_curve";
+};
+
+export type PolarCoords = [
+  radius: number,
+  /** angle in radians */
+  angle: number,
+];
+
+/**
+ * Angles are in radians and centered on 0, 0. Zero radians on a 1 radius circle
+ * corresponds to (1, 0) cartesian coordinates (point), i.e. to the "right".
+ */
+export type SymmetricArc = {
+  radius: number;
+  startAngle: number;
+  endAngle: number;
+};