CPSC170A Assignment 5
Bézier Curves
Extra Credit
Friday, March 8th by 5:00 PM
A Bézier curve is a method for representing curves popularized by the
French engineer Pierre Bézier in the 1960's. Bézier used the curves in
the design automobiles. The curves are still popular today in drawing
and animation applications because they offer an intuitive control
over curve shape. Bézier curves can also be approximated very easily
using a recursive algorithm developed by another Frenchman, Paul de
Casteljau. You are going to create a program that allows users to draw
a Bézier curve.
Details
The program should display a window that adds small circles where ever
the mouse is clicked. Each circle in the window is a control point
for a Bézier curve. Each time a control point is added the display
should redraw the Bézier curve to include the new control point.
In order to draw a Bézier curve, you need to calculate a series of
points on the curve. The program should use a recursive function that
implements the de Casteljau algorithm to calculate a fixed number of
evenly spaced points on the curve. Then, draw lines between each pair
of consecutive points, to draw the curve. The program does not need
to draw the control structure, just the control points and the curve.
The de Casteljau algorithm can be expressed recursively using the
following equations:
dC(⟨ p1⟩ , t) = p1
dC( ⟨ p1, p2, pn ⟩, t) =
dC( ⟨ interp(p1, p2, t),
interp(p2, p3, t),
interp(pn-1, pn, t) ⟩ , t)
Where t is the parametric distance, interp finds the point at the
specified parametric distance between two points, and the angle
brackets, ⟨⟩ , specify a list of points.
Submission: Submit your code as a zip file with your name as the
zip file name on the course Inquire site.
Additional Work
These will not earn you extra credit, but are pretty easy to code if you
feel motivated to do them
Movable Control Points: Add the ability to modify a Bézier curve
after it has been drawn by dragging its control points. When the user
is dragging a control point, the Bézier curve should be redrawn every
time the mouse drag call-back function is called.
Animate de Casteljau: Create an animation of the de Casteljau
algorithm. The program should draw all of the control structures
computed with the de Casteljau algorithm with repeatedly larger values
for t from 0 up to 1 and back down to 0 repeatedly.