Third
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1. Course Introduction to Geometric Modeling ECS 178 WQ 2008 Professor Dr Bernd Hamann Project 3 Interpolation and B Splines Date due Friday Feb 15 2008 demos in the afternoon The third project requires the implementation of algorithms for C1 and C continuous interpolation and B spline curves Your program s must be developed on a workstation or PC or laptop using the OpenGL or a similar library for drawing curves and surfaces and for providing user interface techniques buttons sliders etc You are allowed to use the OpenGL library X windows Motif or the Forms library A user menu must be provided to interactively specify all the parameters required for the various algorithms a Implement the 2D version of the C continuous piecewise cubic interpolation scheme discussed in class computing the de Boor points d first then constructing the B zier points for each cubic curve segment A user specifies the n 1 2D points p i 0 n to be interpolated He she can choose between uniform chord length or centripetal parametrization Your program computes the n 3 points d i 1 n 1 and then constructs the B zier points b j 0 3n Your program must display the polygon defined by the points d the polygon defined by the B zier points bj and the resulting interpolating curve b Implement a 2D version of the de Boor algorithm for evaluating a B spline curve A user specifies the order k2. and the de Boor control points d i 0 n Your program computes the initial knot sequence Up lt Uy lt lt Unix based on the Euclidean distances between the de Boor points as discussed in class Your program displays the original control polygon the entire B spline curve defined over the interval uk 1 Un4i evaluated at a user specified resolution and the knot sequence in form of a knot bar A user must be able to interactively change order control points and knots of a B spline curve c Write a program for performing C continuous quadratic B spline curve interpolation A user specifies a sequence of 2D points to be interpolated and your program computes the sequence of knots and de Boor control points The computation of the control points should follow the principle discussed in class Compute a first control polygon by prescribing the derivative vector at the first point to be interpolated Compute a second control polygon by prescribing a derivative vector at the last point to be interpolated Finally average these two control polygons to obtain the final polygon The final control polygon and the knot sequence must be displayed along with the interpolating quadratic B spline curve A user must be able to change all parameters easily by providing window areas used for the display and manipulation of parameters Regarding the manipulation of control points or points to be interpolated a user must be able to pick such
3. points change their positions in a window and insert delete such points If two or more points are within the same pick region your program must select the point closest to the center of the pick region To move a point in a window use the left and right mouse buttons to change its x and y coordinates Besides having to demonstrate your program prepare a short about one page user s manual explain ing how to use your program DO NOT REMOVE YOUR PROGRAM YOU CAN USE IT FOR FURTHER AS SIGNMENTS HAVE FUN
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