Article

Creative Virtual Tree Modeling Through Hierarchical Topology-Preserving Blending

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We present a new method to efficiently generate a set of morphologically diverse and inspiring virtual trees through hierarchical topology-preserving blending, aiming to facilitate designers’ creativity production. By maintaining the topological consistency of the tree branches, sequences of similar yet different trees and novel intermediate trees with encouragingly interesting structures are generated by performing inner-species and cross-species blending, respectively. Hierarchical fuzzy correspondences are automatically established between two or multiple trees based on the multi-scale topology tree representations. Fundamental blending tasks including morph, grow and wilt are introduced and organized into a tree-structured blending scheduler, which not only introduces the randomness into the blending procedure but also wisely schedules the tasks to generate topology-aware blending sequences, contributing to a variety of resulting trees that exhibit diversities in both geometry and topology. Most significantly, multiple batches of blending can be executed in parallel, resulting in a rapid creation of a large repository of diverse trees.
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... 5 Consequently, topology-aware approaches have been proposed to generate smooth transformations between trees, achieving visually compelling special effects. [6][7][8] However, they do not put explicit efforts into preserving a sequence of morphologically continuous crowns when transforming between trees with specialized crown shapes, leading to less meaningful in-between trees (see Figure 9, top row). ...
... Topology-aware tree animations. Recent works 6,7 have created topologically consistent animations between two topologically varying trees. However, the work of Wang et al. 6 does not handle the animations of foliage. ...
... Recent works 6,7 have created topologically consistent animations between two topologically varying trees. However, the work of Wang et al. 6 does not handle the animations of foliage. Although the work of Wang et al. 7 addresses the smooth transformations of foliage, it fails to preserve the morphological meanings of in-between trees' crowns, leading to less compelling visual effects when transforming between trees with custom crowns. ...
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... Furthermore, the method does not define a proper tree-shape space and a metric. Thus, unlike our approach, tasks such as tree statistics (mean tree) and tree symmetrization cannot be performed with the approach of Wang et al. [2016]. ...
... First, correspondences are found level-wise under the assumption that each tree's trunk has been identified. We will explore in the future the possibility of relaxing this condition using for example fuzzy correspondences as in [Wang et al. 2016]. Second, the proposed framework only considers the tree branches and ignores the tree leaves. ...
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... Finally, there have been a few works that attempted computing smooth deformations between 3D shapes which deform in geometry and topology. Examples include the work of [AXZ * 15] for manmade 3D shapes, and its extension to botanical trees [WXJD17]. These works, however, do not come with a concept of a shape space and a metric. ...
... It also enables characterizing populations of trees with probability distributions, which in turn can be used to generate random instances of 3D botanical trees. These cannot be achieved using previous techniques such as inverse procedural modeling [ŠBM * 10, SPK * 14] or structural blending [WXJD17]. • We develop a mechanism for regressions in the tree-shape space. ...
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... Finally, there have been a few works that attempted computing smooth deformations between 3D shapes which deform in geometry and topology. Examples include the work of [AXZ * 15] for manmade 3D shapes, and its extension to botanical trees [WXJD17]. These works, however, do not come with a concept of a shape space and a metric. ...
... It also enables characterizing populations of trees with probability distributions, which in turn can be used to generate random instances of 3D botanical trees. These cannot be achieved using previous techniques such as inverse procedural modeling [ŠBM * 10, SPK * 14] or structural blending [WXJD17]. • We develop a mechanism for regressions in the tree-shape space. ...
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... In the case of plant modeling, they have been applied to simulate botanical organs, the growing process, and various plant structures. Self-organizing parameter characteristics became the basis of the L-system [22] and self-organizing tree modeling methods [18,28], and we use those characteristics in our approach. Although plausible models have been obtained for the above methods, the final shape of the plant is not easy to control, and many parameters are complex for users to adjust. ...
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Procedural tree models have been popular in computer graphics for their ability to generate a variety of output trees from a set of input parameters and to simulate plant interaction with the environment for a realistic placement of trees in virtual scenes. However, defining such models and their parameters is a difficult task. We propose an inverse modelling approach for stochastic trees that takes polygonal tree models as input and estimates the parameters of a procedural model so that it produces trees similar to the input. Our framework is based on a novel parametric model for tree generation and uses Monte Carlo Markov Chains to find the optimal set of parameters. We demonstrate our approach on a variety of input models obtained from different sources, such as interactive modelling systems, reconstructed scans of real trees and developmental models.
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We introduce set evolution as a means for creative 3D shape modeling, where an initial population of 3D models is evolved to produce generations of novel shapes. Part of the evolving set is presented to a user as a shape gallery to offer modeling suggestions. User preferences define the fitness for the evolution so that over time, the shape population will mainly consist of individuals with good fitness. However, to inspire the user's creativity, we must also keep the evolving set diverse. Hence the evolution is "fit and diverse", drawing motivation from evolution theory. We introduce a novel part crossover operator which works at the finer-level part structures of the shapes, leading to significant variations and thus increased diversity in the evolved shape structures. Diversity is also achieved by explicitly compromising the fitness scores on a portion of the evolving population. We demonstrate the effectiveness of set evolution on man-made shapes. We show that selecting only models with high fitness leads to an elite population with low diversity. By keeping the population fit and diverse, the evolution can generate inspiring, and sometimes unexpected, shapes.
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Assuming that numerical scores are available for the performance of each of n persons on each of n jobs, the "assignment problem" is the quest for an assignment of persons to jobs so that the sum of the n scores so obtained is as large as possible. It is shown that ideas latent in the work of two Hungarian mathematicians may be exploited to yield a new method of solving this problem. 1.
Article
Assuming that numerical scores are available for the performance of each of n persons on each of n jobs, the "assignment problem" is the quest for an assignment of persons to jobs so that the sum of the n scores so obtained is as large as possible. It is shown that ideas latent in the work of two Hungarian mathematicians may be exploited to yield a new method of solving this problem.
Article
Modeling natural elements such as trees in a plausible way, while offering simple and rapid user control, is a challenge. This paper presents a method based on a new structure from silhouettes paradigm. We claim that sketching the silhouettes of foliage at multiple scales is quicker and more intuitive for a user than having to sketch each branch of a tree. This choice allows us to incorporate botanical knowledge, enabling us to infer branches that connect in a plausible way to their parent branch and have a correct distribution in 3D. We illustrate these ideas by presenting a seamless sketch-based interface, used for sketching foliage silhouettes from the scale of an entire tree to the scale of a leaf. Each sketch serves for inferring both the branches at that level and construction lines to serve as support for sub-silhouette refinement. When the user finally zooms out, the style inferred for the branching systems he has refined (in terms of branch density, angle, length distribution and shape) is duplicated to the unspecified branching systems at the same level. Meanwhile, knowledge from botany is again used for extending the branch distribution to 3D, resulting in a full, plausible 3D tree that fits the user-sketched contours. As our results show, this system can be of interest to both experts and novice users. While experts can fully specify all parts of a tree and over-sketch specific branches if required, any user can design a basic 3D tree in one or two minutes, as easily as sketching it with paper and pen.
Article
In this paper, we present a novel continuous field based free-form surface modeling and morphing algorithm. Polyhedra are used in our algorithm as the skeletons of the free-form surfaces. Unlike the conventional methods, we first construct a continuous field from each skeleton using variational interpolation, all these fields are then fused into a global continuous field using blending, warping and boolean operations. The final surface is approximated by the iso-surface of the global field. Based on the field blending operation, our modeling algorithm can easily perform 3D morphing between two arbitrary polyhedra in an intuitive and controllable manner by introducing certain constraints. Several examples are shown to demonstrate that our method can be used to naturally and intuitively model complex free-form surfaces and morph in a controllable way.
Article
This paper has been presented with the Best Paper Award. It will appear in print in Volume 52, No. 1, February 2005.
Conference Paper
ABSTRACT Due to the intrinsic subtlety and dynamics of eye movements, au- tomated generation of natural and engaging,eye motion,has been a challenging task for decades. In this paper we present an effec- tive technique to synthesize natural eye gazes given a head mo- tion sequence as input, by statistically modeling the innate cou- pling between gazes and head movements.,We first simultaneously recorded head motions and eye gazes of human subjects, using a novel hybrid data acquisition solution consisting of an optical mo- tion capture system and off-the-shelf video cameras. Then, we sta- tistically learn gaze-head coupling patterns using a dynamic,cou- pled component analysis model. Finally, given a head motion se- quence as input, we can synthesize its corresponding natural eye gazes based on the constructed gaze-head coupling model. Through comparative user studies and evaluations, we found that comparing with the state of the art algorithms in eye motion synthesis, our ap- proach is more,effective to generate natural gazes correlated with given head motions. We also showed,the effectiveness of our ap- proach for gaze simulation in two-party conversations. Index Terms:,I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Animation; H.5.2 [Information Interfaces and,Presentation]: User Interfaces—Graphical user interfaces (GUI)
Conference Paper
We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are pro- portional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.
Conference Paper
We describe an easily implemented and computationally feasible method for smoothly transitioning from one sampled volumetric model to another. This induces a transition between isosurfaces of the two models. The technique is based on interpolating smoothly between the Fourier transforms of the two volumetric models and then transforming the results back. A linear interpolation between the transformed datasets yields unsatisfactory results in some cases. We use a schedule for the interpolation in which the high frequencies of the first model are gradually removed, the low frequencies are interpolated to those of the second, and the high frequencies of the second model are gradually added in. Such scheduling yields more satisfactory results. We give several examples and comment briefly on preprocessing models to make the morphing smoother.
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In this paper, we describe a method for generating geometric morphs between general 3D solid models. The method is based on the Euclidean skeleton and is capable of generating morphs between shapes that possess different feature sets and different topology. The essential concept that enables the morphing method is utilization of the trimmed skeleton of the symmetric difference as an intermediate shape. The intermediate shape is a valid solid model whose boundary does not self-intersect and is everywhere equidistant from the boundaries of the source shapes. We apply the skeleton-based intermediate shape generation procedure recursively to produce a sequence of shapes, referred to as a morph history, that gradually transform between the initial and target shapes. The method is sufficiently robust to handle significant changes in geometry and topology, such as the creation and annihilation of protrusions, indentations, internal holes and handles, and produces intuitive morph histories.The skeleton also establishes a correspondence between points on the boundaries of the source and target objects. Interpolation between corresponding points is performed to enable fast generation of a morph history consisting of a sequence of valid solid models. For source and target models that are sufficiently close, this interpolative morphing scheme generates results comparable to those obtained by the recursive skeletonization procedure, but with improved computational efficiency. The boundary point correspondence generated by the skeleton enables morphing with surface attributes (e.g., color, texture, surface roughness, and transparency). The skeleton-based procedure also allows for morphing between open curves or surfaces. A modification of the basic procedure allows the user to control the morph by specifying corresponding feature sets on the initial and final objects. Examples are presented to demonstrate the capabilities of the methods described.
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This paper presents a technique for the modelling and rendering of realistic botanical tree images. A strand model is used that is analogous to the internal vascular structure of a tree. The model is “grown” under the simulated influence of gravity and light. The strand densities at each branching point are used to determine branching angles, branch lengths and branch thicknesses, taking into account stored, user definable parameters that characterize the species of tree being modelled. These parameters address such factors as gravimorphism, phototropism, orthotropism, plagiotropism, planartropism and phyllotaxis, and are distributed according to a branch ordering system. Branch segments and joints are modelled by Bézier splines, with an assumed circular cross-section. Leaves are made up from numbers of sample ranges from vector plane equations. The trees are rendered using a surface sampling algorithm with a light Z buffer for shadows and autoregression textures for tree bark and grass.
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This paper considers the problem of computing a constrained edit distance between unordered labeled trees. The problem of approximate unordered tree matching is also considered. We present dynamic programming algorithms solving these problems in sequential timeO(|T 1|×|T 2|×(deg(T 1)+deg(T 2))× log2(deg(T 1)+deg(T 2))). Our previous result shows that computing the edit distance between unordered labeled trees is NP-complete.
Article
We present a semi-automatic and efficient method for producing full polygonal models of range scanned trees, which are initially represented as sparse point clouds. First, a skeleton of the trunk and main branches of the tree is produced based on the scanned point clouds. Due to the unavoidable incompleteness of the point clouds produced by range scans of trees, steps are taken to synthesize additional branches to produce plausible support for the tree crown. Appropriate dimensions for each branch section are estimated using allometric theory. Using this information, a mesh is produced around the full skeleton. Finally, leaves are positioned, oriented and connected to nearby branches. Our process requires only minimal user interaction, and the full process including scanning and modeling can be completed within minutes.
Article
We introduce data-driven suggestions for 3D modeling. Data-driven suggestions support open-ended stages in the 3D modeling process, when the appearance of the desired model is ill-defined and the artist can benefit from customized examples that stimulate creativity. Our approach computes and presents components that can be added to the artist's current shape. We describe shape retrieval and shape correspondence techniques that support the generation of data-driven suggestions, and report preliminary experiments with a tool for creative prototyping of 3D models.
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In this paper, we present a two-level statistical model for characterizing the stochastic and specific nature of trees. At the low level, we define plantons, which are a group of similar organs, to depict tree organ details statistically. At the high level, a set of transitions between plantons is provided to describe the stochastic distribution of organs. Based on such a tree model, we propose a novel tree modeling approach, synthesizing trees by plantons, which are extracted from tree samples. All tree samples are captured from the real world. We have designed a maximum likelihood estimation algorithm to acquire the two-level statistical tree model from single samples or multi- samples. Experimental results show that our new model is capable of synthesizing new trees with similar, yet visually different shapes.
Article
Observation reveals a linear relationship between the logarithm of the circumference of a tree, branch, or leaf stem, and the logarithm of the weight of the tree, branch, or leaf. The bearing of this on the angles of branching in trees is discussed.
Article
We present techniques for realistic real-time rendering of complex landscapes that consist of many highly detailed plant models. The plants are approximated by dynamically changing sets of billboards. Realistic illumination is approximated using spherical harmonics. Since even the rendering of simple billboard cloud plants is too time consuming, the landscape in the background is approximated with shell textures. The combination of these techniques allows us to render large scenes in real-time with varying illumination, which is interesting for computer games and interactive visualization in landscaping and architecture as well as modelling.
Article
In applications dealing with plant growth modeling, increasing attention is being devoted to the topological structure of plants. Different models, based on tree-graphs, have been introduced to represent plants. These models assume that the scale of description is fixed. However, this hypothesis is too restrictive for new modeling applications that aim to tackle analysis or simulation of plant growth at different time and space scales. In order to make such multiscale descriptions available to computer applications, we have defined a general methodology for measuring and representing multiscale plant topological structures. This paper discusses the design of a model of plant topological structures and sketches out its general formal properties. The model supports multiscale, attributed and time-varying descriptions of plants. It is intended to be used for plant analysis methodologies and plant growth simulations.Copyright 1998 Academic Press Limited
Conference Paper
Following the increasing demand to make the creation and manipulation of 3D geometry simpler and more accessible, we introduce a modeling approach that allows even novice users to create sophisticated models in minutes. Our approach is based on the observation that in many modeling settings users create models which belong to a small set of model classes, such as humans or quadrupeds. The models within each class typically share a common component structure. Following this observation, we introduce a modeling system which utilizes this common component structure allowing users to create new models by shuffling interchangeable components between existing models. To enable shuffling, we develop a method for computing a compatible segmentation of input models into meaningful, interchangeable components. Using this segmentation our system lets users create new models with a few mouse clicks, in a fraction of the time required by previous composition techniques. We demonstrate that the shuffling paradigm allows for easy and fast creation of a rich geometric content.
Conference Paper
The authors propose a novel multiresolution-based shape representation for 3D mesh morphing. Our approach does not use combination operations that caused some serious problems in the previous approaches for mesh morphing. Therefore, we can calculate a hierarchical interpolation mesh robustly using two types of subdivision fitting schemes. Our new representation has a hierarchical semiregular mesh structure based on subdivision connectivity. This leads to various advantages including efficient data storage, and easy acquisition of an interpolation mesh with arbitrary subdivision level. We also demonstrate several new features for 3D morphing using multiresolution interpolation meshes
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Traditionally, shape transformation using implicit functions is performed in two distinct steps: 1) creating two implicit functions, and 2) interpolating between these two functions. We present a new shape transformation method that combines these two tasks into a single step. We create a transformation between two N- dimensional objects by casting this as a scattered data interpolation problem in N+1 dimensions. For the case of 2D shapes, we place all of our data constraints within two planes, one for each shape. These planes are placed parallel to one another in 3D. Zero-valued constraints specify the locations of shape boundaries and positivevalued constraints are placed along the normal direction in towards the center of the shape. We then invoke a variational interpolation technique (the 3D generalization of thin-plate interpolation), and this yields a single implicit function in 3D. Intermediate shapes are simply the zero-valued contours of 2D slices through this 3D function. Shape transformation between 3D shapes can be performed similarly by solving a 4D interpolation problem. To our knowledge, ours is the first shape transformation method to unify the tasks of implicit function creation and interpolation. The transformations produced by this method appear smooth and natural, even between objects of differing topologies. If desired, one or more additional shapes may be introduced that influence the intermediate shapes in a sequence. Our method can also reconstruct surfaces from multiple slices that are not restricted to being parallel to one another.
Article
Given two or more objects of general topology, intermediate objects are constructed by a distance field metamorphosis. In the presented method the interpolation of the distance field is guided by a warp function which is controlled by a set of corresponding anchor points. Some rules for defining a smooth least-distorting warp function are given. To reduce the distortion of the intermediate shapes, the warp function is decomposed into a rigid rotational part and an elastic part. The distance field interpolation method is modified so that the interpolation is done in correlation with the warp function. The method provides the animator with a technique, which can be used to create a set of models forming a smooth transition between pairs of a given sequence of keyframe models. The advantage of the new approach is that it is capable of morphing between objects having a different topological genus, and where no correspondence between the geometric primitives of the models need...