We review the treatment of trimmed geometries in the context of design, data exchange, and computational simulation. Such models are omnipresent in current engineering modeling and play a key role for the integration of design and analysis. The problems induced by trimming are often underestimated due to the conceptional simplicity of the procedure. In this work, several challenges and pitfalls are described.

/pdf/a-review-of-trimming-in-isogeometric-analysis-challenges-4bj7mwwi2t.pdf

A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects

An adaptive forward differencing algorithm is presented for rapid rendering of cubic curves and bicubic surfaces. This method adjusts the forward difference step size so that approximately one pixel is generated along an ordinary or rational cubic curve for each forward difference step. The adjustment involves a simple linear transformation on the coefficients of the curve which can be accomplished with shifts and adds. This technique combines the advantages of traditional forward differencing and adaptive subdivision. A hardware implementation approach is described including the adaptive control of a forward difference engine. Surfaces are rendered by drawing many curves spaced closely enough together so that no pixels are left unpainted. A simple curve anti-aliasing algorithm is also presented in this paper. Anti-aliasing cubic curves is supported via tangent vector output at each forward difference step. The adaptive forward differencing algorithm is also suitable for software implementation.

Adaptive forward differencing for rendering curves and surfaces

In this paper we describe an algorithm and hardware for the tessellation of polynomial surfaces. While conventional forward difference-based tessellation is subject to round off error and cracking, our algorithm produces a bit-for-bit consistent triangle mesh across multiple independently tessellated patches. We present tessellation patterns that exploit the efficiency of iterative evaluation techniques while delivering a defect free adaptive tessellation with continuous level-of-detail. We also report the rendering performance of the resulting physical hardware implementation.

/pdf/watertight-tessellation-using-forward-differencing-4z88u5ra2v.pdf

Watertight tessellation using forward differencing

SnakeToonz is an interactive system that allows children and others untrained in cel animation to create two-dimensional cartoons from video streams and images. The ability to create cartoons has traditionally been limited to professional animation houses and trained artists. SnakeToonz aims to give anyone with a video camera and a computer the ability to create compelling cel animation. This is done by combining constraints of the cartooning medium with simple user input and analysis of that input.A cartoon is created in a dialogue with the system. After recording video material the user sketches contours directly onto the first frame of video. These sketches initialize a set of spline-based active contours which are relaxed to best fit the image and other aesthetic constraints. Small gaps are closed, and the user can choose colors for the cartoon. The system then uses motion estimation techniques to track these contours through the image sequence. The user remains in the process to edit the cartoon as it progresses.

/pdf/snaketoonz-a-semi-automatic-approach-to-creating-cel-4qay8qbumy.pdf

SnakeToonz: a semi-automatic approach to creating cel animation from video

For most compute environments, adaptive forward differencing is much more efficient when performed using integer arithmetic than when using floating point. Previously low precision integer methods suffered from serious precision problems due to the error accumulation inherent to forward differencing techniques. This paper proposes several different techniques for implementing adaptive forward differencing using integer arithmetic, and provides an error analysis of forward differencing which is useful as a guide for integer AFD implementation. The proposed technique using 32 bit integer values is capable of rendering curves having more than 4K forward steps with an accumulated error of less than one pixel and no overflow problems. A hybrid algorithm employing integer AFD is proposed for rendering antialiased, texture-mapped bicubic surfaces.

Rendering cubic curves and surfaces with integer adaptive forward differencing

An adaptive forward differencing algorithm is presented for rapid rendering of cubic curves and bicubic surfaces. This method adjusts the forward difference step size so that approximately one pixe...

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Adaptive forward differencing for rendering curves and surfaces