High-quality tree structures modelling using local convolution surface approximation

Zhu, Xiaoqiang; Jin, Xiaogang; You, Lihua

doi:10.1007/s00371-013-0905-2

Cited by 13 publications

(5 citation statements)

References 58 publications

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“…Our current method still leaves room for improvement. Because our goal is to generate visually pleasing morphing effects, issues such as smooth ramifications and collision‐free branches are not explicitly addressed. In terms of the lobe extraction, environmental factors, such as lighting conditions, wind effects, and so forth, should be considered in the future.…”

Section: Resultsmentioning

confidence: 99%

Topologically consistent leafy tree morphing

Wang

Deng

et al. 2017

Computer Animation & Virtual

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We present a novel morphing technique to generate pleasing visual effects between 2 topologically varying trees while preserving the topological consistency and botanical meanings of any in-between shapes as natural trees. Specifically, we first efficiently convert leafy trees into botanically inspired chain-lobe representations in an automatic way. With the aid of branching-pattern aware, one-to-many correspondences between branches and leaves, we hierarchically interpolate branches of in-between trees while maintaining their topological consistencies. Finally, we simultaneously interpolate foliage, specifically every single leaf, during the morphing process, avoiding the generation of unpleasant "floating" leaves. We demonstrate the effectiveness of our approach by creating visually compelling tree morphing animations, even between cross-species.

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Section: Resultsmentioning

confidence: 99%

Topologically consistent leafy tree morphing

Wang

Deng

et al. 2017

Computer Animation & Virtual

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“…As described in Zhu et al, the weight of some line segments can be deduced as follows to approximate the cylindrical shapes with a given support radius R i (Figure (a)). If the distance from the iso‐surface passing point p to the line skeleton is d , the weight λ i can be calculated by the following equation:

\begin{matrix} right F (boldp) & left = 2 λ_{i} \int_{0}^{\sqrt{R_{_{i}}^{2} - d_{i}^{2}}} {(1 - \frac{d_{i}^{2} + x^{2}}{R_{i}^{2}})}^{2} d x & right = T, \\ left \Rightarrow λ_{i} = \frac{15 T R_{i}^{4}}{16 {(R_{i}^{2} - d_{i}^{2})}^{\frac{5}{2}}}, \end{matrix}

under the condition of

d_{i} = \frac{R_{i}}{2}

λ_{i} = \frac{10 \sqrt{3} T}{9 R_{i}}

.…”

Section: Convolution Approximation Of Skeletons With Varying Radii Onmentioning

confidence: 99%

Brush2Model: Convolution surface‐based brushes for 3D modelling in head‐mounted display‐based virtual environments

Zhu

Song

You

et al. 2017

Computer Animation & Virtual

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Easy and efficient 3D modelling in virtual environments is an important and unsolved topic. This paper proposes a new modelling approach to tackle this issue. It invents convolution surface-based brushes to directly draw 3D models in head-mounted display-based virtual environments. In order to maximize the efficiency, flexibility, and capacity of our proposed modelling approach, we propose three different skeleton-based convolution surfaces to tackle different modelling tasks: point skeleton-based convolution surfaces for metaball shapes, line skeleton-based convolution surfaces for cylindrical shapes, and polygon skeleton-based convolution surfaces for planar surfaces. Their combination makes 3D modelling more flexible and powerful. The high efficiency is further raised by our developed closed-form solutions for point skeletons, ends of line skeletons, and edges of polygonal skeletons. Different user-friendly sweeping schemes are provided to facilitate intuitive inputs for various complex shape generation. Unlike Google's Tilt Brush, which is used to create disconnected sheet-like surfaces only, our proposed convolution surface-based brushes can produce smoothly blended manifold surfaces, and novice users can easily learn and use them to create various interesting 3D models efficiently. KEYWORDS brush-based 3D modelling, convolution surfaces, closed-form analytical solutions, HMD-based virtual environments Comput Anim Virtual Worlds. 2017;28:e1764.wileyonlinelibrary.com/journal/cav

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“…Offset curves are widely used in various computer-aided design and manufacturing (CAD/CAM) areas, such as tool path generation [1,2], 3D numerical control (NC) machining [3,4], solid modeling [5], graphics [6], and so on. However, the offset curve usually cannot be represented in a polynomial or rational form, and thus is difficult to apply in CAD systems.…”

Section: Introductionmentioning

confidence: 99%

A Novel Method of Offset Approximation along the Normal Direction with High Precision

Zhao

Zhou

2017

MCA

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Abstract:A new algorithm is proposed for polynomial or rational approximation of the planar offset curve. The best rational Chebyshev approximation could be regarded as a kind of geometric approximation along the fixed direction. Based on this idea, we developed a wholly new offset approximation method by changing the fixed direction to the normal directions. The error vectors follow the direction of normal, and thus could reflect the approximate performance more properly. The approximation is completely independent of the original curve parameterization, and thus could ensure the stability of the approximation result. Experimental results show that the proposed algorithm is reasonable and effective.

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High-quality tree structures modelling using local convolution surface approximation

Cited by 13 publications

References 58 publications

Topologically consistent leafy tree morphing

Topologically consistent leafy tree morphing

Brush2Model: Convolution surface‐based brushes for 3D modelling in head‐mounted display‐based virtual environments

A Novel Method of Offset Approximation along the Normal Direction with High Precision

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