# Difference between revisions of "Vertex Post-Processing"

OpenGL Rendering Pipeline

Vertex Post-Processing is the stage in the OpenGL Rendering Pipeline where the vertex outputs of the Vertex Processing undergo a variety of operations. Many of these are setup for Primitive Assembly and Rasterization stages.

## Clipping

Primitives generated by previous stages are collected and then clipped to the view volume. Each vertex has a clip-space position (the gl_Position​ output of the last Vertex Processing stage). The viewing volume for a vertex is defined by:

{\begin{aligned}-w_{c}&\leq x_{c}&\leq w_{c}\\-w_{c}&\leq y_{c}&\leq w_{c}\\-w_{c}&\leq z_{c}&\leq w_{c}\end{aligned}}

This volume can be modified by depth clamping as well as the addition of user-defined clip-planes. The total volume that primitives are clipped to, including user-defined clip planes, is the clipping volume.

The way primitives are clipped to this clipping volume depends on the basic Primitive type:

Points
Points are not really "clipped". If a point is in any way outside of the clipping volume, then the primitive is discarded (ie: not rendered). Points can be bigger than one pixel, but the clipping remains; if the center of the point (the actual gl_Position​ value) is outside of the clipping range, it is discarded. Yes, this means that point sprites will disappear when the center moves off-screen.
Platform Issue (NVIDIA): These cards will not clip points "properly". That is, they will do what people generally want (only discard the point if it is fully off-screen), rather than what the OpenGL specification requires. Be advised that other hardware does what OpenGL asks.
Lines
If the line is entirely outside of the volume, it is discarded. If the line is partially outside of the volume, then it is clipped; new vertex coordinates are computed for one or both vertices, as appropriate. The end-point of such a clipped vertex is on the boundary of the clipping volume.
Triangles
A triangle is clipped to the viewing volume by generating appropriate triangles who's vertices are on the boundary of the clipping volume. This may generate more than 1 triangle, as appropriate. If a triangle is entirely outside of the viewing volume, it is culled.

When primitives are clipped, new per-vertex outputs must be generated for them. These are generated via linear interpolation (in clip-space) of the output values. Flat-shaded outputs don't get this treatment.

### Depth clamping

The clipping behavior against the Z position of a vertex (ie: $-w_{c}\leq z_{c}\leq w_{c}$) can be turned off by activating depth clamping. This is done with . This will cause the clip-space Z to remain unclipped by the front and rear viewing volume.

Note: With perspective projections, you still get clipping with the sides of the viewing volume. Depth clamping turns a frustum into a pyramid. So objects that go behind the camera are still clipped; it's just objects between the projection near-plane and the camera who's clipping is turned off.

The Z value computations will proceed as normal through the pipeline. After computing the window-space position, the resulting Z value will be clamped to the .

## Perspective divide

The clip-space positions returned from the clipping stage are transformed into normalized device coordinates (NDC) via this equation:

${\begin{pmatrix}x_{{ndc}}\\y_{{ndc}}\\z_{{ndc}}\end{pmatrix}}={\begin{pmatrix}{\tfrac {x_{c}}{w_{c}}}\\{\tfrac {y_{c}}{w_{c}}}\\{\tfrac {z_{c}}{w_{c}}}\end{pmatrix}}$

## Viewport transform

The viewport transform defines the transformation of vertex positions from NDC space to window space. These are the coordinates that are rasterized to the output image.

The viewport is defined by a number of viewport parameters. These parameters are set by these functions:

void (GLint x​, GLint y​, GLsizei width​, GLsizei height​) void (GLdouble nearVal​, GLdouble farVal​)

void (GLfloat nearVal​, GLfloat farVal​)

The second two functions set the same parameters, the near and far values of the depth range.

Given the viewport parameters, we compute the window-space coordinates via these equations:

{\begin{pmatrix}x_{w}\\y_{w}\\z_{w}\end{pmatrix}}={\begin{pmatrix}{\begin{aligned}{\tfrac {width}{2}}x_{{ndc}}&+x+{\tfrac {width}{2}}\\{\tfrac {height}{2}}y_{{ndc}}&+y+{\tfrac {height}{2}}\\{\tfrac {farVal-nearVal}{2}}z_{{ndc}}&+{\tfrac {farVal+nearVal}{2}}\end{aligned}}\end{pmatrix}}

Where x​, y​, width​, height​, nearVal​, and farVal​ are the viewport parameters.

### Viewport array

Core in version 4.5 4.1 ARB_viewport_array

Multiple viewports can be used in OpenGL. The specific viewport for a particular primitive can be set by the Geometry Shader. If the GS does not specify a viewport, then viewport number 0 is selected. The computation works as above, except where it says "the viewport parameters", it means "the viewport parameters for the primitive's viewport index".

There are sets of viewports, indexed on the half-open range [0, GL_MAX_VIEWPORTS). Each index has its own depth range and viewport coordinates. The previously defined functions will only set the value for viewport index 0.

To set the viewport parameters for a particular index, use this pair of functions:

void (GLuint index​, GLfloat x​, GLfloat y​, GLfloat w​, GLfloat h​) void (GLuint index​, const GLfloat *v​)

void (GLuint index​, GLdouble nearVal​, GLdouble farVal​)

The index​ is the viewport index to set the parameters for. takes an array of 4 floats, in the same orders as the parameters for .

Multiple viewport indices can be set with a single function, via these APIs:

void (GLuint first​, GLsizei count​, const GLfloat *v​) void (GLuint first​, GLsizei count​, const GLdouble *v​)

The first​ index is the first viewport index to set. count​ is the number of viewport indices to be set by the function. v​ is an array of viewport values, which contains count​ * 4 or 2 values, depending on the function being called. The values for a single viewport index are in the same order as the arguments in the regular function calls.