OpenGL Programming Guide

Chapter 13Now That You Know

Cheap Image Transformation

Suppose you want to draw a distorted version of a bitmapped image (perhaps simply stretched or rotated, or perhaps drastically modified by some mathematical function). In many cases, you can achieve good results by drawing the image of each pixel as a quadrilateral. Although this scheme doesn't produce images as nice as those you would get by applying a sophisticated filtering algorithm (and it might not be sufficient for sophisticated users), it's a lot quicker.

To make the problem more concrete, assume that the original image is m pixels by n pixels, with coordinates chosen from [0, m-1] × [0, n-1]. Let the distortion functions be x(m,n) and y(m,n). For example, if the distortion is simply a zooming by a factor of 3.2, then x(m,n) = 3.2*m and y(m,n) = 3.2*n. The following code draws the distorted image:

glShadeModel(GL_FLAT);
glScale(3.2, 3.2, 1.0);
for (j=0; j < n; j++) {
    glBegin(GL_QUAD_STRIP);
    for (i=0; i <= m; i++) {
        glVertex2i(i,j);
        glVertex2i(i, j+1);
        set_color(i,j);
    }
    glEnd();
}

This code draws each transformed pixel in a solid color equal to that pixel's color and scales the image size by 3.2. The routine set_color() stands for whatever the appropriate OpenGL command is to set the color of the image pixel.

The following is a slightly more complex version that distorts the image using the functions x(i,j) and y(i,j):

glShadeModel(GL_FLAT);
for (j=0; j < n; j++) {
    glBegin(GL_QUAD_STRIP);
    for (i=0; i <= m; i++) {
        glVertex2i(x(i,j), y(i,j));
        glVertex2i(x(i,j+1), y(i,j+1));
        set_color(i,j);
    }
    glEnd();
}

An even better distorted image can be drawn with the following code:

glShadeModel(GL_SMOOTH);
for (j=0; j < (n-1); j++) {
    glBegin(GL_QUAD_STRIP);
    for (i=0; i < m; i++) {
        set_color(i,j);
        glVertex2i(x(i,j), y(i,j));
        set_color(i,j+1);
        glVertex2i(x(i,j+1), y(i,j+1));
    }
    glEnd();
}

This code smoothly interpolates color across each quadrilateral. Note that this version produces one fewer quadrilateral in each dimension than do the flat-shaded versions because the color image is being used to specify colors at the quadrilateral vertices. In addition, you can antialias the polygons with the appropriate blending function (GL_SRC_ALPHA, GL_ONE) to get an even nicer image.

OpenGL Programming Guide