how to perform shearing of a rectangle in OpenGL - c++

Question

I am using OpenGL apis to obtain isometric view of Rectangle using SSR (Scale/Shear/Rotate) method. I am able to scale and rotate rectangle. But I not getting way as how to shear a rectangle. I am new to OpenGL. Please help.
#include <gl\glut.h> // glut.h must come before gl.h and glu.h
#include <gl\gl.h>
#include <gl\glu.h>
void display()
{
glClear(GL_COLOR_BUFFER_BIT);
glBegin(GL_QUADS);
glVertex2f(20, 20);
glVertex2f(20, 70);
glVertex2f(70, 70);
glVertex2f(70, 20);
glEnd();
glScalef(0.86,0.86,0.86);
glTranslatef(200,0,0);
glRotatef(30, 0, 0,1);
glBegin(GL_QUADS);
glVertex2f(20, 20);
glVertex2f(20, 70);
glVertex2f(70, 70);
glVertex2f(70, 20);
glEnd();
glFlush();
}
void init()
{
glClearColor(0.5,0.5,0.0, 0.0);
glColor3f(1,0,0);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrtho(0, // left
800, // right
800, // bottom
0, // top
0, // zNear
1 // zFar
);
}
void main(int argc, char** argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);
glutInitWindowSize(900, 1080);
glutInitWindowPosition(0, 0);
glutCreateWindow("Simple");
glutDisplayFunc(display);
init();
glutMainLoop();
}

Answer 1

For a shear parallel to the x-axis by the amount shear:
GLfloat m[16] = {
1.0f, 0.0f, 0.0f, 0.0f,
shear, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f
};
glMultMatrixf(m);
and parallel to the y-axis:
GLfloat m[16] = {
1.0f, shear, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 0.0f, 1.0f
};
glMultMatrixf(m);
When you compare this to matrices specified in mathematical notation, e.g. the Wikipedia Shear matrix page, keep in mind that OpenGL matrices are specified in column major order.
Both of the above are for transformations in the 2D plane. I.e. the first one leaves the x-axis stationary, and shears the y-axis, while the second one keeps the y-axis stationary, and shears the x-axis. If you look at shear transforms in full 3D space, you get many more variations.