Capsule light volume is made of a sphere divided into two and extruded along the capsules segment to form the cylindrical part of the capsule. As with the point light volume, we will use the tessellator to generate the capsule volume, only this time we will expend two control points instead of one. Each one of these points will eventually get turned into a half sphere attached to half of the capsules cylindrical part. The two capsule halves will connect at the center of the capsule.
Our capsule will be scaled by two values, a range and a segment length. Those are the exact same values we used for the forward capsule light. Unfortunately, we can't use a matrix to scale the capsule because we need to scale the segment and the range separately. Therefore, we will set the capsule lights range, segment length, and a transformation to projected space to the Domain shader. The matrix will combine the capsule rotation and translation with the view and projection matrix...