ellipsograph
tool to construct ellipses based on the parametric equations x = a cos(t), y = b sin(t)

parametric equations of circles, ellipses and Lissajou figures - R.F.Barrow
plotter for x=Acos(Bt) and y=Ccos(Dt)

Cubic spline and Bezier curves - Consider the end point (a,b) and its control point (c,d) and the end point (g,h) and its control point (e,f). The spline curve is given by the parametric equations:

x=at³+3ct²(1-t)+3et(1-t)²+g(1-t)³
y=bt³+3dt²(1-t)+3ft(1-t)²+h(1-t)³

• interactive Bezier spline
• description of Bezier curves
• geometric interpretation of spline curve
• Bezier curve editor with continuity correction
• Bezier curve editor with continuity hint
• Winplot file for cubic spline

Visual Dictionary of Special Plane Curves - Xah Lee
descriptions, properties, graphics, animations, links

Classic Curves - Paul Bourke
equations and sample graphs

cycloid generator - Maths Online

roller coasters and the cycloid
One-half of a cycloid upside-down gives the roller coaster's track that will yield the shortest possible time for the ride.

spirograph 1
Change the radii and offset by sliders and watch the wheel turn. Values are given for a cardioid, astroid, rose, vertical line, ellipse, spiral, ...

spirograph 2
Change the radii and offset by sliders and see the result instantly. The connection between the equations and the spirograph are explained.

spirograph 3
Small wheel moves inside a larger wheel. Adjust the number of teeth for each wheel and the offset and watch the wheel turn.

gallery of 3 dimensional surfaces - pictures and equations

resources page - conic sections

resources page - algebra - other resources