Analysis And Research On Frame Interpolation Algorithm Of Space Curve

The frame of space curves and interpolation issues play an important role in computergraphics, and have been widely applied in real life such as computer animation, robottrajectory planning, and appearance designing. At present, research for frame interpolation isnot a lot in domestic or overseas. Existing methods are relatively more complex, lessaccurate and not universal. Therefore, study of frame interpolation method is of greatsignificance and value.Frame interpolation problem is to generate a curve through a number of given points byinterpolation and the directions of frames in the curve are consistent with the directions ofgiven frames. In fact, the problem is to find a free curve through the data points at the sametime under the premise of direction constraint of frame vector on the free surface. A solutionhas been given to solve this problem. Firstly, we get the control points by solving linearequations reversely and then generate a cubic non-uniform B-spline curve by interpolation ofthe given points. Secondly, rotation-minimizing adapted frames in the interpolation curvecan be calculated by solving differential equation. When the directions of frames in the curveare not consistent with the directions of given frames, we use the iterative method to renewthe control points, to make the direction of each vector of the frame in the curve beconsistent with the given frame. In the mean time we need to take measures to ensure thedata points stay in the curve after changing, and eventually get the satisfying curvedemanded.We test this method in different samples. It turns out that the algorithm can obtaincorrect results whether the sample size is more or less. The algorithm is not only applied tothe two-dimensional curves, but also can be used to interpolate other types of frame.