Affine transformations preserving a parabola / Robin Houston

Public

Edited

Nov 1, 2020

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md`# Affine transformations preserving a parabola

cy = 5

{

const ct = canvas.ct;

ct.save();

ct.clearRect(0, 0, WIDTH, HEIGHT);

ct.translate(cx, HEIGHT - cy);

ct.transform(50, 0, 0, -50, 0, 0);

ct.transform(1, 2*t, 0, 1, t, t*t);

const max_x = Math.floor((WIDTH - cx) / 50);

const max_y = Math.floor((HEIGHT - cy) / 50);

ct.beginPath();

for (let y = -max_y; y <= max_y * 2; y++) {

ct.moveTo(-max_x-1, y);

ct.lineTo(max_x+1, y);

}

for (let x = -max_x; x <= max_x; x++) {

ct.moveTo(x, -max_y);

ct.lineTo(x, max_y * 2);

}

ct.lineWidth = 1/50;

ct.strokeStyle = "#999";

ct.stroke();

ct.beginPath();

ct.moveTo(-Math.sqrt(max_y * 2), max_y * 2);

ct.quadraticCurveTo(0, -max_y * 2, Math.sqrt(max_y * 2), max_y * 2);

ct.lineWidth = 3/50;

ct.strokeStyle = "red";

ct.stroke();

ct.restore();

return this || html`(<i>the drawing function</i>)`;

}

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