By J. Chen, E. Wegman
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Extra resources for Foundations of 3D Graphics Programming
The result is a composition of translations, rotations, and scalings. We will study this through the following three examples. Example 1: Find the coordinates of a moving clock hand in 2D. Consider a single clock hand. The center of rotation is given at c(x0, y0), and the end rotation point is at h(x1, y1). If we know the rotation angle is θ, can we find the new end point h' after the rotation? As shown in Fig. 5, we can achieve this by a series of transformations. 1. Translate the hand so that the center of rotation is at the origin.
SetAutoSwapBufferMode(false). swapBuffers() manually. What often happens is that a frame is too complicated to draw in 1/60 second. If this happens, each frame in the frame buffer is displayed more than once and the display refresh rate is still 1/60. However, the image frame rate is much lower, and the animation could be jittering. The image frame rate depends on how fast frames of images are scan-converted, which corresponds to the rate of finishing drawing in the frame buffer. To achieve smooth animation, we need high-performance algorithms as well as graphics hardware to carry out many graphics functions efficiently.
The intensities in the table are precalculated according to the filter we use and the width of the line. The following is an implementation of scan-converting an antialiased line. If we assume the distance from the current pixel to the line is D, then the distances from the E, S, N, and NE pixels can be calculated, respectively. The distances are shown in Fig. 4. ) We can modify Bresenham’s algorithm to scan-convert an antialiased line. The distances from the pixels closest to the line are calculated iteratively.