Why OpenGL cut off polygons (even if this settings is disabled)? - c++

Question

I read similar suggested questions and their solutions, but could not find an answer.
I'm trying to draw a scene with an isometric view in OpenGL.
Draw func:
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glRotatef(atan(0.5f) * 180.0f / PI, 1.0f, 0.0f, 0.0f);
glRotatef(-45.0f, 0.0f, 1.0f, 0.0f);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glBegin(GL_QUADS);
glColor3f(1.0f, 1.0f, 1.0f);
glVertex3f(0.0f, 0.0f, 0.0f);
glVertex3f(1.0f, 0.0f, 0.0f);
glVertex3f(1.0f, 0.0f, 1.0f);
glVertex3f(0.0f, 0.0f, 1.0f);
glEnd();
glPopMatrix();
In the end, I get this result. The camera does have an isometric projection, but for some reason polygons are clipped.
If I add glTranslatef(-0.8f, 0, -0.8f) before drawing the quad, the result is as follows:
The problem is that I don't apply any optimization to OpenGL render. But why do polygons have to be cut off?

Answer 1

The polygons are clipped by the near or far plane of the viewing volume.
When you do not set a projection matrix, then view space, clip space and normalized device space are the same. The normalized device space is a unique cube with the left, bottom, near of (-1, -1, -1) and right, top, far of (1, 1, 1). All the geometry which is not inside this cube is clipped.
Actually you draw a quad with a side length of 1. One vertex of the quad is at the origin of the view (0, 0, 0). The quad is rotated around the origin by glRotate. Since the length of the diagonal of the quad is sqrt(2.0), one vertex of the rotated quad is clipped by either the near plane or the far plane.
If you construct and rotate a quad whose center is (0, 0 ,0), it will not be clipped, because the length form the center to each vertex is sqrt(2.0)/2.0. That is less than 1 (distance to near and far plane form the center of the viewing volume)
glBegin(GL_QUADS);
glColor3f(1.0f, 1.0f, 1.0f);
glVertex3f(-0.5f, 0.0f, -0.5f);
glVertex3f( 0.5f, 0.0f, -0.5f);
glVertex3f( 0.5f, 0.0f, 0.5f);
glVertex3f(-0.5f, 0.0f, 0.5f);
glEnd();
respectively
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glRotatef(atan(0.5f) * 180.0f / PI, 1.0f, 0.0f, 0.0f);
glRotatef(-45.0f, 0.0f, 1.0f, 0.0f);
glTranslate(-0.5f, 0.0f, -0.5f);
glBegin(GL_QUADS);
glColor3f(1.0f, 1.0f, 1.0f);
glVertex3f(0.0f, 0.0f, 0.0f);
glVertex3f(1.0f, 0.0f, 0.0f);
glVertex3f(1.0f, 0.0f, 1.0f);
glVertex3f(0.0f, 0.0f, 1.0f);
glEnd();
Alternatively you can set an Orthographic projection, which enlarges the viewing volume by glOrtho:
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glOrtho(-1.0, 1.0, -1.0, 1.0, -2.0, 2.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glRotatef(atan(0.5f) * 180.0f / PI, 1.0f, 0.0f, 0.0f);
glRotatef(-45.0f, 0.0f, 1.0f, 0.0f);
glBegin(GL_QUADS);
glColor3f(1.0f, 1.0f, 1.0f);
glVertex3f(0.0f, 0.0f, 0.0f);
glVertex3f(1.0f, 0.0f, 0.0f);
glVertex3f(1.0f, 0.0f, 1.0f);
glVertex3f(0.0f, 0.0f, 1.0f);
glEnd();