We present a new method for user controlled morphing of two homeomorphic triangle meshes of arbitrary topology. In particular we focus on the problem of establishing a correspondence map between source and target meshes. Our method employs the MAPS algorithm to parameterize both meshes over simple base domains and an additional harmonic map bringing the latter into correspondence. To control the mapping the user specifies any number of feature pairs, which control the parameterizations produced by the MAPS algorithm. Additional controls are provided through a direct manipulation interface allowing the user to tune the mapping between the base domains. We give several examples of sthetically pleasing morphs which can be created in this manner with little user input. Additionally we demonstrate examples of temporal and spatial control over the morph.

this article, we emphasize practical issues; an earlier survey by Bern and Eppstein [24] emphasized theoretical results. Although there is inevitably some overlap between these two surveys, we intend them to be complementary.

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Algorithms for summation and dot product of floating point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or K-fold working precision, K 3. For twice the working precision our algorithms for summation and dot product are some 40 % faster than the corresponding XBLAS routines while sharing similar error estimates. Our algorithms are widely applicable because they require only addition, subtraction and multiplication of floating point numbers in the same working precision as the given data. Higher precision is unnecessary, algorithms are straight loops without branch, and no access to mantissa or exponent is necessary.

In this paper we describe a method for computing approximate results of boolean operations (union, intersection, difference) applied to free-form solids bounded by multiresolution subdivision surfaces.

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A quad-double number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of significand. We present the algorithms for various arithmetic operations (including the four basic operations and various algebraic and transcendental operations) on quad-double numbers. The performance of the algorithms, implemented in C++, is also presented. 1.

In two dimensions, a constrained Delaunay triangulation (CDT) respects a set of segments that constrain the edges of the triangulation, while still maintaining most of the favorable properties of ordinary Delaunay triangulations (such as maximizing the minimum angle). CDTs solve the problem of enforcing boundary conformity---ensuring that triangulation edges cover the boundaries (both interior and exterior) of the domain being modeled. This paper discusses the three-dimensional analogue, constrained Delaunay tetrahedralizations (also called CDTs), and their advantages in mesh generation. CDTs maintain most of the favorable properties of ordinary Delaunay tetrahedralizations, but they are more difficult to work with, because some sets of constraining segments and facets simply do not have CDTs. However, boundary conformity can always be enforced by judicious insertion of additional vertices, combined with CDTs. This approach has three advantages over other methods for boundary recovery: it usually requires fewer additional vertices to be inserted, it yields provably good bounds on edge lengths (i.e. edges are not made unnecessarily short), and it interacts well with provably good Delaunay refinement methods for tetrahedral mesh generation.

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Let P be a polyhedral subdivision in R 3 with a total of n faces. We show that there is an embedding oe of the vertices, edges, and facets of P into a subdivision Q, where every vertex coordinate of Q is an integral multiple of 2 \Gammadlog 2 n+2e . For each face f of P , the Hausdorff distance in the L1 metric between f and oe(f) is at most 3/2. The embedding oe preserves or collapses vertical order on faces of P . The subdivision Q has O(n 4 ) vertices in the worst case, and can be computed in the same time. 1 Introduction Geometric algorithms are usually described in the "real-number RAM" model of computation, where arithmetic operations on real numbers have unit cost. A programmer implementing a geometric algorithm must find some substitution for real arithmetic. The substitution of exact arithmetic on a subset of the reals, say the integers or the rationals, avoids the difficulties that can arise from naive substitution of floating-point arithmetic [4, 12, 14, 15]. The subs...