Curve Renderers

This page documents library functions that render curves, such as circles and ellipses.

Circle

Generate a circle at centre $p_\text{centre}$ with radius $r$.

Arguments

Return

Usage

Circles cannot be rendered by a function – an expression is needed. Compare the output of the renderer to $0$ using an inequality to render the circle.

d_{circle}\left(p_{centre},\ r,\ x,\ y\right)=\left(x-p_{centre}.x\right)^{2}+\left(y-p_{centre}.y\right)^{2}-r^{2}
d_{circle}\left(\left(2,\ 2\right),\ 1,\ x,\ y\right)\le0
d_{circle}\left(\left(5,\ 5\right),\ 10,\ x,\ y\right)\ge0

Implementation

For all points $(x, y)$ in the 2D plane, the renderer evaluates the formula of a circle with $(x, y)$ substituted in. Using an inequality renders the locus of points that form the circle.

Dependencies

None

Ellipse

Generate an ellipse at centre centre $p_\text{centre}$ with radii $p_\text{radii}$.

Arguments

Return

Usage

Circles cannot be rendered by a function – an expression is needed. Compare the output of the renderer to $0$ using an inequality to render the circle.

d_{ellipse}\left(p_{centre},\ p_{radii},\ x,\ y\right)=\left(\frac{x-p_{centre}.x}{p_{radii}.x/p_{radii}.y}\right)^{2}+\left(y-p_{centre}.y\right)^{2}-p_{radii}.y^{2}
d_{ellipse}\left(\left(0,\ 0\right),\ R,\ x,\ y\right)\le0
R=\left(X,\ Y\right)
X=3
Y=2

Implementation

Essentially, we’re drawing a circle with radius $p_\text{radii}.y$, then scaling it by the ratio $p_\text{radii}.x / p_\text{radii}.y$ to form the ellipse.

Dependencies

None