We present a novel point-based rendering approach based on object-space point interpolation. We introduce the concept of a transformation-invariant covariance matrix of a set of points to efficiently determine splat sizes in a multiresolution hierarchy. We analyze continuous point interpolation in object-space, and define a new class of parametrized blending kernels to achieve smooth blending. Furthermore, we present a hardware accelerated rendering algorithm based on α -texture mapping and α -blending.