OpenGL Viewport Transform (original) (raw)

Related Topics: OpenGL Transformation, OpenGL Projection Matrix

Overview
NDC to Window Coordinates

Overview

The last step of vertex operations in OpenGL is viewport transform converting the normalized device coordinates (NDC) to window (screen) coordinates in order to map the NDC to the 2D screen. Note that the window coordinates still keep the Z coordinate for the depth testing during the fragment operations later.
ndc to window coord

OpenGL provides 2 functions to specify the 2D rectangle of the rendering screen and the depth range. glViewport() is to set the viewport of the window, and glDepthRange()/glDepthRangef() is to map the depth values from NDC to window coordinates.


glViewport(X, Y, W, H)
glDepthRangef(N, F)

The parameters of these functions are;

X: the left corner of the viewport
Y: the bottom corner of the viewport
W: the width of the viewport
H: the height of the viewport
N: the near clipping value, 0 by default
F: the far clipping value, 1 by default

NDC to Window Coordinates

The viewport transform from NDC, NDC to window coordinates, window coords is solving a line equation with 2 known points.

map x_n to x_w

Map xn to xw

line equation for X

map y_n to y_w

Map yn to yw

line equation for Y

map z_n to z_w

Map zn to zw

line equation for z

Therefore, the conversion formula for all 3 coordinates together;
NSC to window coords

Or, 4x4 viewport transform matrix is;