23.2.2 Spotlight Effect

The spotlight effect evaluates to one of three possible values, depending on whether the light is actually a spotlight and whether the vertex lies inside or outside the cone of illumination produced by the spotlight:

• 1 if the light isn't a spotlight (GL_SPOT_CUTOFF is 180.0).
• 0 if the light is a spotlight but the vertex lies outside the cone of illumination produced by the spotlight.
• $(\max \{v \cdot d, 0\})^{GL\_SPOT\_EXPONENT}$ where: v = (v_x, v_y, v_z) is the unit vector that points from the spotlight (GL_POSITION) to the vertex.

  d = (d_x,d_y,d_z) is the spotlight's direction (GL_SPOT_DIRECTION), assuming the light is a spotlight and the vertex lies inside the cone of illumination produced by the spotlight.

  The dot product of the two vectors v and d varies as the cosine of the angle between them; hence, objects directly in line get maximum illumination, and objects off the axis have their illumination drop as the cosine of the angle.

To determine whether a particular vertex lies within the cone of illumination, OpenGL evaluates $(\max \{\hat{v} \cdot \hat{d}, 0\})$ where $\hat{v}$ and $\hat{d}$ are as defined above. If this value is less than the cosine of the spotlight's cutoff angle (GL_SPOT_CUTOFF), then the vertex lies outside the cone; otherwise, it's inside the cone.