Universal Index Formula of Parameterized Combination Operator for Eco-environmental Quality Evaluation

[Objective] The aim was to evaluate the regional eco-environmental quality by using the universal index formula of parameterization combination operator based normalized index values.[Method] Through setting reference values and normalized transformation formulae for typical ecological environmental indexes appropriately,the difference among the standard normalized values would become very small after normalized transformation,and the ecological environmental indices expressed by normalized values can be equivalent to normalized indices.Under certain optimization conditions,shuffled frog leaping based on immune evolutionary particle swarm optimization algorithm was applied to optimize the parameters in parameterization combination operator formula,and the universal index formula suited to eco-environmental quality assessment was established finally.[Result] The universal index formula of parameterization combination operator,appropriate for any m(1≤m≤23) ecological environmental indices,was used to assess the eco-environmental quality of towns surrounding Headland Reservoir,and the results were in full accordance with those of unascertained measure method,that is,the eco-environmental quality of five towns around Headland Reservoir was the fourth grade.[Conclusion]The universal index formula of parameterization combination operator,suited to eco-environmental quality evaluation,is simple and intuitive in form,easy in computation and universal in application.

ARAP++:an extension of the local/global approach to mesh parameterization

Mesh parameterization is one of the fundamental operations in computer graphics(CG) and computeraided design(CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible(ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting Jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties(angle and area)of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.