During tracing of a primary ray in a 3-D space (e.g., a 3-D scene in graphics rendering), a ray is found to intersect a primitive (e.g., a triangle) located in the 3-D space. Secondary ray(s) may be generated for a variety of purposes. For example, occlusion rays may be generated to test occlusion of a point of intersection between the primary ray and primitive is illuminated by any of the light(s). An origin for each secondary ray can be modified from the intersection point based on characteristics of the primitive intersected. For example, an offset from the intersection point can be calculated using barycentric coordinates of the intersection point and interpolation of one or more parameters associated with vertices defining the primitive. These parameters may include a size of the primitive and differences between a geometric normal for the primitive and a respective additional vector supplied with each vertex.