Topologically consistent trimmed surface approximations based on triangular patches Original Research Article

A scheme to approximate the trimmed surfaces defined by two tensor-product surface patches, intersecting in a smooth curve segment that extends between diametrically opposite patch corners, is formulated. The trimmed surface approximations are specified by triangular Bézier patches, whose tangent planes agree precisely with those of the tensor-product surfaces along the two sides where they coincide. Topological consistency of the two trimmed surfaces is achieved by requiring the “hypotenuse” sides of the triangular patches to be coincident. In the case of bicubic tensor-product patches and quintic triangular trimmed surface approximations, enforcing these conditions entails the solution of a linear system of 30 equations in 32 unknowns. The two remaining scalar freedoms, together with four additional free control points, are employed to enhance the accuracy and/or smoothness properties of the intersection curve and trimmed surface approximations. By means of an appropriate subdivision preprocessing, the trimmed surface scheme may be used on models described by arbitrary bicubic surface patches.