How to Draw Quarter‑Circle Arcs in a Physics Engine with SVG and Matter.js

Drawing a Quarter‑Circle Arc in a Physics Engine

When a project requires a quarter‑circle arc inside a physics engine, the most flexible approach is to define the shape with SVG and then import it into the engine.

SVG Path Commands

M x y : move the pen to point (x, y).

L x y : draw a straight line from the current point to (x, y).

H x : draw a horizontal line to x.

V y : draw a vertical line to y.

A rx ry x-axis-rotation large-arc-flag sweep-flag x y : draw an elliptical arc to (x, y).

C x1 y1, x2 y2, x y : cubic Bézier curve.

S x2 y2, x y : smooth cubic Bézier curve (first control point omitted).

Q x1 y1, x y : quadratic Bézier curve.

T x y : smooth quadratic Bézier curve (control point omitted).

Z : close the current path.

Understanding the A (Arc) Command

Draws an elliptical arc to (x, y) with radii rx and ry. x-axis-rotation rotates the ellipse around the x‑axis. large-arc-flag = 0 draws the smaller (<180°) arc; = 1 draws the larger (>180°) arc. sweep-flag = 0 draws the arc counter‑clockwise; = 1 draws it clockwise.

Example of a quarter‑circle arc in the lower‑left corner: M80 80 A45 45 0 0 0 125 125 L128 80 Z The path starts at (80, 80), draws a 45 px radius arc to (125, 125) (small arc, counter‑clockwise), then closes the shape with a line to (128, 80).

For a concave (inward) quarter‑circle, adjust the sweep flag to 1 (clockwise) and modify the line connection point accordingly.

Converting SVG to a Physics Engine

Using matter.js, the Svg.pathToVertices method transforms the SVG path into a set of vertices that the engine can simulate.

After conversion, the vertices can be added to a Matter.js body, allowing the quarter‑circle arc to participate in collisions and other physics interactions.