linear phase difference change:

x = sin(theta + phasetheta);

y = cos(theta)

and

x = sin(thetax);

y = cos(thetay);

are equivalent forms, assuming thetax has a different delta than thetay. What's important is the *ratio* of theta to phasetheta (or thetax to thetay). When the ratio is a simple fraction, the shape is simple and predictable; ratios that aren't simple fractions (e.g. .51) tend to produce elaborate net-like shapes.

trig phase difference change:

x = sin(theta)

y = cos(theta + sin(phasetheta));

Again, it's the ratio between the deltas that matters. Incrementing theta by .1 and phasetheta by .01 will have the same effect as .2 and .02.

original:

static double rad = .25;

double ox = sin(theta + sin(phasetheta) + i);

double oy = cos(theta2);

m_View->SetNormOrigin(ox * rad +.35, oy * rad +.35, FALSE);

theta += .01;

theta2 += .02;

phasetheta += .0311;

slower and better:

static double rad = .25;

double ox = sin(theta + sin(phasetheta));

double oy = cos(theta2);

m_View->SetNormOrigin(ox * rad +.35, oy * rad +.35, FALSE);

theta += .001;

theta2 += .002;

phasetheta += .00211;

## Saturday, June 25, 2005

### lissajous origin

constant phase difference: affects width of oval, difference of PI/2 gives a line

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