When interpolating a data mesh using triangular Bezier patches, the requirement of C1 or G1 continuity imposes strict constraints on the control points of adjacent patches. However, fulfilment of these continuity constraints cannot guarantee that the resulting surfaces have good shape. This thesis presents an approach to constructing surfaces with approximate C 1/G1 continuity, where a small amount of discontinuity is allowed between surface normals of adjacent patches. For all the schemes presented in this thesis, although the resulting surface has C1/G1 continuity at the data vertices, I only require approximate C1/ G1 continuity along data triangle boundaries so as to lower the patch degree.;For functional data, a cubic interpolating scheme with approximate C1 continuity is presented. In this scheme, one cubic patch will be constructed for each data triangle and upper bounds are provided for the normal discontinuity across patch boundaries. For a triangular mesh of arbitrary topology, two interpolating parametric schemes are devised.;For each data triangle, the first scheme performs a domain split and constructs three cubic micro-patches; the second scheme constructs one quintic patch for each data triangle. To reduce the normal discontinuity, neighbouring patches across data triangle boundaries are adjusted to have identical normals at the middle point of the common boundary. The upper bounds for the normal discontinuity between two parametric patches are also derived for the resulting approximate G1 surface.;In most cases, the resulting surfaces with approximate continuity have the same level of visual smoothness and in some cases better shape quality.
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