13 Drawing Lines over Polygons and Using Polygon Offset
It's difficult to render coplanar primitives in OpenGL for two reasons:
- Given two overlapping coplanar primitives with different vertices, floating point round-off errors from the two polygons can generate different depth values for overlapping pixels. With depth test enabled, some of the second polygon's pixels will pass the depth test, while some will fail.
- For coplanar lines and polygons, vastly different depth values for common pixels can result. This is because depth values from polygon rasterization derive from the polygon's plane equation, while depth values from line rasterization derive from linear interpolation.
Setting the depth function to GL_LEQUAL or GL_EQUAL won't resolve the problem. The visual result is referred to as stitching, bleeding, or Z fighting.
Polygon offset was an extension to OpenGL 1.0, and is now incorporated into OpenGL 1.1. It allows an application to define a depth offset, which can apply to filled primitives, and under OpenGL 1.1, it can be separately enabled or disabled depending on whether the primitives are rendered in fill, line, or point mode. Thus, an application can render coplanar primitives by first rendering one primitive, then by applying an offset and rendering the second primitive.
While polygon offset can alter the depth value of filled primitives in point and line mode, under no circumstances will polygon offset affect the depth values of GL_POINTS, GL_LINES, GL_LINE_STRIP, or GL_LINE_LOOP primitives. If you are trying to render point or line primitives over filled primitives, use polygon offset to push the filled primitives back. (It can't be used to pull the point and line primitives forward.)
Because polygon offset alters the correct Z value calculated during rasterization, the resulting Z value, which is stored in the depth buffer will contain this offset and can adversely affect the resulting image. In many circumstances, undesirable "bleed-through" effects can result. Indeed, polygon offset may cause some primitives to pass the depth test entirely when they normally would not, or vice versa. When models intersect, polygon offset can cause an inaccurate rendering of the intersection point.
Polygon offset allows the application to specify a depth offset with two parameters, factor and units. factor scales the maximum Z slope, with respect to X or Y of the polygon, and units scales the minimum resolvable depth buffer value. The results are summed to produce the depth offset. This offset is applied in screen space, typically with positive Z pointing into the screen.
The factor parameter is required to ensure correct results for filled primitives that are nearly edge-on to the viewer. In this case, the difference between Z values for the same pixel generated by two coplanar primitives can be as great as the maximum Z slope in X or Y. This Z slope will be large for nearly edge-on primitives, and almost non-existent for face-on primitives. The factor parameter lets you add this type of variable difference into the resulting depth offset.
A typical use might be to set factor and units to 1.0 to offset primitives into positive Z (into the screen) and enable polygon offset for fill mode. Two passes are then made, once with the model's solid geometry and once again with the line geometry. Nearly edge-on filled polygons are pushed substantially away from the eyepoint, to minimize interference with the line geometry, while nearly planar polygons are drawn at least one depth buffer unit behind the line geometry.
The 1.0 polygon offset extension didn't let you apply the offset to filled primitives in line or point mode. Only filled primitives in fill mode could be offset.
In the 1.0 extension, a bias parameter was added to the normalized (0.0 - 1.0) depth value, in place of the 1.1 units parameter. Typical applications might obtain a good offset by specifying a bias of 0.001.
See the GLUT example, which renders two cylinders, one using the 1.0 polygon offset extension and the other using the 1.1 polygon offset interface.
Polygon offset, as its name implies, only works with polygonal primitives. It affects only the filled primitives: GL_TRIANGLES, GL_TRIANGLE_STRIP, GL_TRIANGLE_FAN, GL_QUADS, GL_QUAD_STRIP, and GL_POLYGON. Polygon offset will work when you render them with glPolygonMode set to GL_FILL, GL_LINE, or GL_POINT.
Polygon offset doesn't affect non-polygonal primitives. The GL_POINTS, GL_LINES, GL_LINE_STRIP, and GL_LINE_LOOP primitives can't be offset with glPolygonOffset().
You can simulate the effects of polygon offset by tinkering with glDepthRange(). For example, you might code the following:
glDepthRange (0.1, 1.0); /* Draw underlying geometry */ glDepthRange (0.0, 0.9); /* Draw overlying geometry */
This code provides a fixed offset in Z, but doesn't account for the polygon slope. It's roughly equivalent to using glPolygonOffset with a factor parameter of 0.0.
You can render coplanar primitives with the Stencil buffer in many creative ways. The OpenGL Programming Guide outlines one well-know method. The algorithm for drawing a polygon and its outline is as follows:
- Draw the outline into the color, depth, and stencil buffers.
- Draw the filled primitive into the color buffer and depth buffer, but only where the stencil buffer is clear.
- Mask off the color and depth buffers, and render the outline to clear the stencil buffer.
On some SGI OpenGL platforms, an application can use the SGIX_reference_plane extension. With this extension, the user specifies a plane equation in object coordinates corresponding to a set of coplanar primitives. You can enable or disable the plane. When the plane is enabled, all fragment Z values will derive from the specified plane equation. Thus, for any given fragment XY location, the depth value is guaranteed to be identical regardless of which primitive rendered it.