Study On The Theory And Methods Of Digital Bas-relief Design Based On Object Model

Bas-Relief is widely used in packaging, shapes decoration, coinage industry. Digital bas-reliefdesign based on2D images and sketches is not proper for high-detailed bas-relief, due to thecomplicated processes and abstract representation of model. In recent years, with the development of3D measurement technology and digital geometry processing technology, digital bas-relief designfrom3D model is becoming to a hot research spot in the field of CAD. In this paper, an intensivestudy based on the discrete differential geometry and digital geometry processing technology iscarried out on the theory and methods of digital bas-relief design from3D object models, Definitionsof digital bas-relief are proposed in view of the bas-relief structure and the design process respectively,which are suitable for bas-relief design from3D digital models. Afterwards, four contents arethoroughly studied including planar bas-relief design, curved surface bas-relief design, line-basedbas-relief design and bas-relief reapplication.The main contents and innovations are summarized as follows:Two algorithms for planar bas-relief design are proposed in spatial domain of geometry signal. Oneis based on shape features decomposition, the other is based on differential coordinate deformation.For the first one, a shape is decomposed into one base part and two detailed parts at different scalesusing low-pass filtering and Laplace-Beltrima operator, subsequently, a detail-preserving bas-relief isachieved efficiently by applying different compression manner to those parts accordingly. For thesecond one, the object bas-relief is expressed to the optimum solution of a Poisson equation with thefixed boundary condition implicitly by using differential coordinate which measured the localgeometry shape. These two methods solved the resample disadvantage of the existing bas-reliefgeneration algorithm. The experiments show that relief generated by methods in this paper is betterthan the relief obtain by resample method if they have the same number of vertices.The first try to design the plane bas-relief in frequency domain is made in this paper, twoalgorithms are provided including an algorithm based on manifold harmonic transforming and analgorithm based on Fourier transforming. For the first one, the geometry signal is transformed fromspatial domain to frequency domain by using the eigenfunctions of manifold harmonic transformingas a set of orthogonal basis. And then the signal is divided into high frequency and low frequency bygeometry frequency cutting method raised in this paper. By compressing the two bands respectivelyand using the inverse manifold harmonic transform, a bas-relief is obtained. Even for the modelwithout too much detail feature or mesh with low resolution, the algorithm can still support a good result. For the second one, shape is compressed by high-pass filter on the frequency domain after FFT.After that, discontinuity in shape is further detected based on proposed absolute variation function andthen eliminated. By the process, a bas-relief is finally generated. The second method is quite efficient,and has a better result for the model with strong edge feature.A detail preserving curved surface bas-relief algorithm is provided in this paper. In this method, thegeneration of curved surface bas-relief is converted to a constrained least squares equation whichguaranteed surfaces of object relief has the first order geometry continuity at the boundary where itintersection with the background surface. Canny operator, bilateral filter, unsharp masking are actingon the gradient domain of source model in order to fulfill the aim of detail preserving. Thestereoscopic impression of relief can be toned by the relaxation factor of the constrain condition. Thealgorithm properly solved the smooth blending problem, the generated relief has a fine detail, andfurthermore, it has a well control of the relief’s shape feature under the system parameters.A line-style bas-relief generation method is proposed by this paper. The main procedure includes:vision-dependent feature point extraction, separate-and-connect-based skeleton extraction operatorbased feature point optimize, feature line extraction with a user selected line width and depth rangecompression. The relief generated by this algorithm has a good visual effect and properly conveyedthe shape of source model.A relief paste algorithm based on normal adjustment is proposed to handle the repeated work inbas-relief design. The algorithm’s input includes an original relief model and a target model, and theoutput is a new relief composed from them. The main process includes parametric corresponding,relief mapping and normal-adjustment. This algorithm decreases the deformation during the reliefpasting process, and supports a new solution for rapid relief design based on the existed relief model.