Nephroid curve as an envelope (with concurrent rays)
- Zoltán Kovács
Equation of the nephroid curve is usually a sixth order algebraic curve. It is constructed by mirroring concurrent rays to the edge of the circle.
Similar curves can be drawn when the rays are parallel. Here they are concurrent, that is they come from the near point-like source D.
- Drag the point D (redisplaying the nephroid curve can be a little bit slow). It can be moved only to grid points. Interesting types of points are: outside the circle, on the circle, inside the circle.
- What is the difference between the outputs when D=(-3,0) and D=(-2,0)?
- Try to explain what happens when D is in the origin.
- Can you classify the points inside the circle concerning the choice of D? (You can zoom in by using Shift and the mouse wheel or move the canvas with Shift+dragging.)