Parametric Surfaces

By Charles Xie

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A parametric surface is a 3D surface defined by a set of parametric equations with two parameters, usually denoted as u and v.

How to draw seashells

A seashell surface is a surface made by a circle which spirals up the z-axis while decreasing its own radius and distance from the z-axis. It can be defined parametrically as:

x = [u/(2πR)]cos(Nu)[1+cos(v)]
y = [u/(2πR)]sin(Nu)[1+cos(v)]
z = [u/(2πR)]sin(v)+H[u/(2π)]P

where R is the radius, N is the number of turns, H is the height, and P is the power. You can adjust these parameters to make different types of seashells such as a nautilus.

With iFlow, you can use a Parametric Equation Block in conjunction with a Surface3D block to create a diagram that can generate the seashell surface. You can also use global variables to allow users to adjust the control parameters such that the shape can be altered.

Click HERE to play with the above example

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