Space-Time Transfinite Interpolation of Volumetric Material Properties

The paper presents a novel technique based on extension of a general mathematical method of transfinite interpolation to solve an actual problem in the context of a heterogeneous volume modelling area. It deals with time-dependent changes to the volumetric material properties (material density, colour and others) as a transformation of the volumetric material distributions in space-time accompanying geometric shape transformations such as metamorphosis. The main idea is to represent the geometry of both objects by scalar fields with distance properties, to establish in a higher-dimensional space a time gap during which the geometric transformation takes place, and to use these scalar fields to apply the new space-time transfinite interpolation to volumetric material attributes within this time gap. The proposed solution is analytical in its nature, does not require heavy numerical computations and can be used in real-time applications. Applications of this technique also include texturing and displacement mapping of time-variant surfaces, and parametric design of volumetric microstructures

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

Application of 3D animation principles and tools in geometrical education

Geometrical education using 3D animation principles and tools represents a new methodology approach and its final result is presented on new way, as multimedia tool. The originality of the paper is based on interdisciplinary approach and use of new technologies. The method derived from the overlap of multiple disciplines such as architecture, structural systems, descriptive geometry, computer animation and programming. Teamwork is comprised of different disciplines since the authors working in different domains of architectural studies. This paper is presented as a visual dynamic educational tool for students of technical and applied arts faculties. The aim is to simplify the perception of geometric forms and the process of their construction. The results leads to the production of geometry with complex topology and could be more developed. So, the results are multilayered, and are the solid basis for further scientific research and further development in practice. The geometrical education target group is the students of the technical and art faculties. It is necessary to emphasize that this work is the beginning of our further scientific research papers in different areas due to an interdisciplinary approach. These areas are: geometrical education, pedagogical theory and psychological aspects of teaching and experimental design in architecture. Aspects and research results presented in this paper are: the basic structure of multimedia learning aid, production methodology, and the final application in education

Application of 3D animation principles and tools in geometrical education

Geometrical education using 3D animation principles and tools represents a new methodology approach and its final result is presented on new way, as multimedia tool. The originality of the paper is based on interdisciplinary approach and use of new technologies. The method derived from the overlap of multiple disciplines such as architecture, structural systems, descriptive geometry, computer animation and programming. Teamwork is comprised of different disciplines since the authors working in different domains of architectural studies. This paper is presented as a visual dynamic educational tool for students of technical and applied arts faculties. The aim is to simplify the perception of geometric forms and the process of their construction. The results leads to the production of geometry with complex topology and could be more developed. So, the results are multilayered, and are the solid basis for further scientific research and further development in practice. The geometrical education target group is the students of the technical and art faculties. It is necessary to emphasize that this work is the beginning of our further scientific research papers in different areas due to an interdisciplinary approach. These areas are: geometrical education, pedagogical theory and psychological aspects of teaching and experimental design in architecture. Aspects and research results presented in this paper are: the basic structure of multimedia learning aid, production methodology, and the final application in education

A framework for automatic and perceptually valid facial expression generation

Facial expressions are facial movements reflecting the internal emotional states of a character or in response to social communications. Realistic facial animation should consider at least two factors: believable visual effect and valid facial movements. However, most research tends to separate these two issues. In this paper, we present a framework for generating 3D facial expressions considering both the visual the dynamics effect. A facial expression mapping approach based on local geometry encoding is proposed, which encodes deformation in the 1-ring vector. This method is capable of mapping subtle facial movements without considering those shape and topological constraints. Facial expression mapping is achieved through three steps: correspondence establishment, deviation transfer and movement mapping. Deviation is transferred to the conformal face space through minimizing the error function. This function is formed by the source neutral and the deformed face model related by those transformation matrices in 1-ring neighborhood. The transformation matrix in 1-ring neighborhood is independent of the face shape and the mesh topology. After the facial expression mapping, dynamic parameters are then integrated with facial expressions for generating valid facial expressions. The dynamic parameters were generated based on psychophysical methods. The efficiency and effectiveness of the proposed methods have been tested using various face models with different shapes and topological representations