Study And Application Of Conformal Geometric Algebra Based Multi-dimensional Surface Intersection Algorithm

Triangulated surfaces intersection operation has been widely used in geometric modeling, computer-aided design, GIS spatial analysis and3D geological modeling. The operation based on traditional computational geometry has some shortcomings. For example, the method is not always intuitively clear; the geometric operation is inconsistent with the mathematical calculation when dealing with different geometrical objects, and it is relatively difficult to be expanded to high dimension and so on. This thesis introduces the conformal geometric algebra theory, and tries to build the framework of a unified expression and operation of different types and different dimensional geometric objects, and then implements multi-dimensional integrated structure of triangulated surfaces intersection algorithm and changes detection algorithm based thereon. Finally, the accuracy, validity and geographical interpretation of mentioned algorithms are discussed thro ugh the typical case studies.Based on the framework of conformal geometric algebra multi-dimensionally-unified representation and computation, the thesis develops ways to divide and reconstruct the multi-dimensional geographic objects, and implements expressions and storage mechanism based on multivector are implemented, according to the geographical modeling and application requirements. And then, taking into account requirements of geographical spatial analysis, the thesis builds the index of the multi-dimensional space object for computing and retrieval mechanism, thus achieving effective division, retrieval and analysis of multi-dimensional objects using the basic operational rules defined in the algebraic space and computing space constructed by basic operators.Using the multi-dimensional unified objects expression and operation structure of conformal geometric algebra as reference, and meeting the need of the surface intersection algorithm, the thesis achieves the detection of triangular facets intersect and intersection computation, and proposes multi-dimensional integrated structure of triangulation surface intersection algorithm framework, and build a change detection. Based on the surface intersection algorithm, the forementioned algorithms which unify the involved expression of different dimensions objects and basic topology, provide new technogical supporting the expression and simulation of geographical objects The research also provides new potential ways to extend the unified multidimensional spatial analysis methods. Multi-dimensional Surface Intersection Algorithm is realized by Antarctic ice sheet’s simulation data. And then based on results from intersection operation, the thesis triangle-reconstructs surface with local constraints, extracts the change region, calculates the factors-area and volume, and detects Antarctic ice’s variation tendency. The Antarctic icecap’s simulation case study shows that the surface change-detection algorithm of this paper has better ability in detection, and it indicates that the surface change detection algorithm based CGA’S Surface Intersection has good generality and potential replication. It provides an effective reference to build an efficient, multi-dimensional integration geographic space analysis algorithm...