With the help of the development team in PYXIS Inc., our research has been integrated in Worldview ( https://www.worldview.gallery/PYXIS ) (see the below figure).

With the help of the development team in PYXIS Inc., our research has been integrated in [https://www.worldview.gallery/|PYXIS Worldview] (see the below figure).

http://pages.cpsc.ucalgary.ca/~amahdavi/pmwiki-2.2.8/uploads/Main/wv.jpg

http://pages.cpsc.ucalgary.ca/~amahdavi/pmwiki-2.2.8/uploads/Main/wv.jpg

http://pages.cpsc.ucalgary.ca/~amahdavi/pmwiki-2.2.8/uploads/Main/wv.jpg

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/wv.png

With the help of the development team in PYXIS Inc., our research has been integrated in PYXIS Worldview (see the below figure). In PYXIS worldview, data sets from different resources and different formats can be integrated together for the purpose of data analysis, visualization, etc. Currently, PYXIS worldview is successfully used in educational environments and we hope that we can release a version for the public use in the near future. Having, such a goal in mind, many new research areas needed to be investigated such as data transmission, compression, etc.

[1] ACM: Atlas of Connectivity Maps, Ali Mahdavi-Amiri, 2015 http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%%

[1] ACM: Atlas of Connectivity Maps, Ali Mahdavi-Amiri, 2015 [http://theses.ucalgary.ca/handle/11023/2247?mode=full&submit_simple=Show+full+item+record| http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png]]

PhD Thesis

[1] ACM: Atlas of Connectivity Maps, Ali Mahdavi-Amiri, 2015 http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%%

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/hex-con-maps-jde2014-mahdavi-amiri.png

Geospatial data is gathered through a variety of different methods. The integration and handling of such data-sets within a Digital Earth framework are very important in many aspects of science and engineering. One means of addressing these tasks is to use a Geodesic Discrete Global Grid System and map points of the Earth’s surface to cells. An indexing mechanism is needed to access the data and handle data queries within these cells.. In [4], we present a general hierarchical indexing mechanism for hexagonal cells resulting from the refinement of triangular spherical polyhedra representing the Earth. In this work, we establish a 2D hexagonal coordinate system and diamond-based hierarchies for hexagonal cells that enables efficient determination of hierarchical relationships for various hexagonal refinements, and demonstrate its usefulness in Digital Earth frameworks. See [4] for more details.

Digital Earth frameworks provide a tool to receive, send and interact with large location-based data sets, organized usually according to Discrete Global Grid Systems (DGGS). In DGGS, an indexing method is used to assign a unique index to each cell of a global grid and the data sets corresponding to these cells are retrieved or allocated using this unique index. There exist many methods to index cells of DGGS. Toward facility, interoperability, and also defining a “standard” for DGGS, a conversion is needed to translate a data set from one DGGS to another. In [5], we first propose a categorization of indexing methods of DGGS and then define a general conversion method from one indexing to another. Several examples are presented to describe the method. See [5] for more details.

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/hex-con-maps-jde2014-mahdavi-amiri.png

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/indexing-of-dggs-ijgi2015-mahdavi-amiri.jpg

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/indexing-of-dggs-ijgi2015-mahdavi-amiri.jpg

[4] Hexagonal Connectivity Maps for Digital Earth, Ali Mahdavi-Amiri, Erika Harrison, Faramarz Samavati International Journal of Digital Earth, (2014) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png?
[5] Categorization and Conversions for Indexing Methods of Discrete Global Grid Systems, Ali Mahdavi-Amiri, Faramarz Samavati, Perry Peterson, ISPRS International Journal of Geo-Information, (2015) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png?

[5] Categorization and Conversions for Indexing Methods of Discrete Global Grid Systems, Ali Mahdavi-Amiri, Faramarz Samavati, Perry Peterson, ISPRS International Journal of Geo-Information, 2015, http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png?

[4] Hexagonal Connectivity Maps for Digital Earth, Ali Mahdavi-Amiri, Erika Harrison, Faramarz Samavati International Journal of Digital Earth, 2014, http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png?
[5] Categorization and Conversions for Indexing Methods of Discrete Global Grid Systems, Ali Mahdavi-Amiri, Faramarz Samavati, Perry Peterson ISPRS International Journal of Geo-Information, 2015, http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png?

[4] Hexagonal Connectivity Maps for Digital Earth, Ali Mahdavi-Amiri, Erika Harrison, Faramarz Samavati International Journal of Digital Earth, 2013, http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png?

[4] Hexagonal Connectivity Maps for Digital Earth, Ali Mahdavi-Amiri, Erika Harrison, Faramarz Samavati International Journal of Digital Earth, 2013, http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[4] Hexagonal Connectivity Maps for Digital Earth, Ali Mahdavi-Amiri, Erika Harrison, Faramarz Samavati International Journal of Digital Earth, 2013, http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[3] Optimization of inverse Snyder polyhedral projection, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, International Conference on Cyberworlds (CW), in association with ACM SIGGRAPH and Eurographics, IEEE Computer Society, pp. 136-143 (Oct 2011) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[4] Hexagonal Connectivity Maps for Digital Earth, Ali Mahdavi-Amiri, Erika Harrison, Faramarz Samavati International Journal of Digital Earth, 2013, http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[3] Hexagonal Connectivity Maps for Digital Earth, Ali Mahdavi-Amiri, Erika Harrison, Faramarz Samavati International Journal of Digital Earth, 2013, http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

Digital Earth frameworks provide a tool to receive, send and interact with large location-based data sets, organized usually according to Discrete Global Grid Systems (DGGS). In DGGS, an indexing method is used to assign a unique index to each cell of a global grid and the data sets corresponding to these cells are retrieved or allocated using this unique index. There exist many methods to index cells of DGGS. Toward facility, interoperability, and also defining a “standard” for DGGS, a conversion is needed to translate a data set from one DGGS to another. In [5], we first propose a categorization of indexing methods of DGGS and then define a general conversion method from one indexing to another. Several examples are presented to describe the method

Geospatial data is gathered through a variety of different methods. The integration and handling of such data-sets within a Digital Earth framework are very important in many aspects of science and engineering. One means of addressing these tasks is to use a Geodesic Discrete Global Grid System and map points of the Earth’s surface to cells. An indexing mechanism is needed to access the data and handle data queries within these cells.. In [4], we present a general hierarchical indexing mechanism for hexagonal cells resulting from the refinement of triangular spherical polyhedra representing the Earth. In this work, we establish a 2D hexagonal coordinate system and diamond-based hierarchies for hexagonal cells that enables efficient determination of hierarchical relationships for various hexagonal refinements, and demonstrate its usefulness in Digital Earth frameworks.

Digital Earth Workshop, September 13-14, 2014

Digital Earth Workshop, September 13-14, 2014

The digital Earth framework is a multiresolution 3D model used to visualize location-based data. In [1], we introduce a new digital Earth framework using a cube as its underlying polyhedron. To create multiresolution, we introduce two types of 1-to-2 refinement. Having a smaller factor of refinement enables us to provide more resolutions and therefore a smoother transition among resolutions. We also suggest two indexing methods specifically designed for quadrilateral cells resulting from 1-to-2 refinement. We finally discuss the equal area spherical projection that we are using in this framework to model the Earth as a sphere partitioned to equal area cells. See [1] for more details.

Related Papers

[1] Equal Area Spherical Subdivision, Erika Harrison, 2012 http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%%

Modern area preserving projections employed by cartographers and geographers have closed forms when transitioning between the sphere and the plane. Inversions - from the planar map to the spherical approximation of the Earth - are slower, requiring iterative root finding approaches or entirely undetermined. Recent optimizations of the common Inverse Snyder Equal Area Polyhedral projection have been fairly successful, however the work herein improves it further by adjusting the approximating polynomial. An evaluation against the original and improved optimizations is provided, along with a previously unexplored real-time analysis. See [2] for further details.

Modern techniques in area preserving projections used by cartographers and other geospatial researchers have closed forms when projecting from the sphere to the plane, as based on their initial derivations. Inversions, from the planar map to the spherical approximation of the Earth which are important for modern 3D analysis and visualizations, are slower, requiring iterative root finding approaches, or not determined at all. We introduce optimization techniques for Snyder’s inverse polyhedral projection by reducing iterations, and using polynomial approximations for avoiding them entirely. Results including speed up, iteration reduction, and error analysis are provided. For additional details, see [3].

The digital Earth framework is a multiresolution 3D model used to visualize location-based data. In [1], we introduce a new digital Earth framework using a cube as its underlying polyhedron. To create multiresolution, we introduce two types of 1-to-2 renement. Having a smaller factor of refinement enables us to provide more resolutions and therefore a smoother transition among resolutions. We also suggest two indexing methods specifically designed for quadrilateral cells resulting from 1-to-2 refinement. We finally discuss the equal area spherical projection that we are using in this framework to model the Earth as a sphere partitioned to equal area cells. See [1] for more details.

Modern area preserving projections employed by cartographers and geographers have closed forms when transitioning between the sphere and the plane. Inversions - from the planar map to the spherical approximation of the Earth - are slower, requiring iterative root finding approaches or entirely undetermined. Recent optimizations of the common Inverse Snyder Equal Area Polyhedral projection have been fairly successful, however the work herein improves it further by adjusting the approximating polynomial. An evaluation against the original and improved optimizations is provided, along with a previously unexplored real-time analysis. See [2] for more details.

Modern techniques in area preserving projections used by cartographers and other geospatial researchers have closed forms when projecting from the sphere to the plane, as based on their initial derivations. Inversions, from the planar map to the spherical approximation of the Earth which are important for modern 3D analysis and visualizations, are slower, requiring iterative root finding approaches, or not determined at all. We introduce optimization techniques for Snyder’s inverse polyhedral projection by reducing iterations, and using polynomial approximations for avoiding them entirely. Results including speed up, iteration reduction, and error analysis are provided. See [3] for more details.

[1] One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%
[2] Analysis of inverse Snyder optimizations, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, Transactions on Computational Science XVI, LNCS 7380, Springer Berlin Heidelberg, pp. 134-148 (2012) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%
[3] Optimization of inverse Snyder polyhedral projection, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, International Conference on Cyberworlds (CW), in association with ACM SIGGRAPH and Eurographics, IEEE Computer Society, pp. 136-143 (Oct 2011) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[1] One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%
[2] Analysis of inverse Snyder optimizations, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, Transactions on Computational Science XVI, LNCS 7380, Springer Berlin Heidelberg, pp. 134-148 (2012) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%
[3] Optimization of inverse Snyder polyhedral projection, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, International Conference on Cyberworlds (CW), in association with ACM SIGGRAPH and Eurographics, IEEE Computer Society, pp. 136-143 (Oct 2011) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[1] One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[2] Analysis of inverse Snyder optimizations, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, Transactions on Computational Science XVI, LNCS 7380, Springer Berlin Heidelberg, pp. 134-148 (2012) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[3] Optimization of inverse Snyder polyhedral projection, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, International Conference on Cyberworlds (CW), in association with ACM SIGGRAPH and Eurographics, IEEE Computer Society, pp. 136-143 (Oct 2011) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[1] One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[1] One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%% >>?

The digital Earth framework is a multiresolution 3D model used to visualize location-based data. In [1], we introduce a new digital Earth framework using a cube as its underlying polyhedron. To create multiresolution, we introduce two types of 1-to-2 renement. Having a smaller factor of refinement enables us to provide more resolutions and therefore a smoother transition among resolutions. We also suggest two indexing methods specifically designed for quadrilateral cells resulting from 1-to-2 refinement. We finally discuss the equal area spherical projection that we are using in this framework to model the Earth as a sphere partitioned to equal area cells.

Modern area preserving projections employed by cartographers and geographers have closed forms when transitioning between the sphere and the plane. Inversions - from the planar map to the spherical approximation of the Earth - are slower, requiring iterative root finding approaches or entirely undetermined. Recent optimizations of the common Inverse Snyder Equal Area Polyhedral projection have been fairly successful, however the work herein improves it further by adjusting the approximating polynomial. An evaluation against the original and improved optimizations is provided, along with a previously unexplored real-time analysis.

Modern techniques in area preserving projections used by cartographers and other geospatial researchers have closed forms when projecting from the sphere to the plane, as based on their initial derivations. Inversions, from the planar map to the spherical approximation of the Earth which are important for modern 3D analysis and visualizations, are slower, requiring iterative root finding approaches, or not determined at all. We introduce optimization techniques for Snyder’s inverse polyhedral projection by reducing iterations, and using polynomial approximations for avoiding them entirely. Results including speed up, iteration reduction, and error analysis are provided.

Modern techniques in area preserving projections used by cartographers and other geospatial researchers have closed forms when projecting from the sphere to the plane, as based on their initial derivations. Inversions, from the planar map to the spherical approximation of the Earth which are important for modern 3D analysis and visualizations, are slower, requiring iterative root finding approaches, or not determined at all. We introduce optimization techniques for Snyder’s inverse polyhedral projection by reducing iterations, and using polynomial approximations for avoiding them entirely. Results including speed up, iteration reduction, and error analysis are provided.

Modern area preserving projections employed by cartographers and geographers have closed forms when transitioning between the sphere and the plane. Inversions - from the planar map to the spherical approximation of the Earth - are slower, requiring iterative root finding approaches or entirely undetermined. Recent optimizations of the common Inverse Snyder Equal Area Polyhedral projection have been fairly successful, however the work herein improves it further by adjusting the approximating polynomial. An evaluation against the original and improved optimizations is provided, along with a previously unexplored real-time analysis.

The digital Earth framework is a multiresolution 3D model used to visualize location-based data. In [1], we introduce a new digital Earth framework using a cube as its underlying polyhedron. To create multiresolution, we introduce two types of 1-to-2 renement. Having a smaller factor of refinement enables us to provide more resolutions and therefore a smoother transition among resolutions. We also suggest two indexing methods specifically designed for quadrilateral cells resulting from 1-to-2 refinement. We finally discuss the equal area spherical projection that we are using in this framework to model the Earth as a sphere partitioned to equal area cells.

[1] One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%% [2] Analysis of inverse Snyder optimizations, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, Transactions on Computational Science XVI, LNCS 7380, Springer Berlin Heidelberg, pp. 134-148 (2012) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%% [3] Optimization of inverse Snyder polyhedral projection, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, International Conference on Cyberworlds (CW), in association with ACM SIGGRAPH and Eurographics, IEEE Computer Society, pp. 136-143 (Oct 2011) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

[1] Equal Area Spherical Subdivision, Erika Harrison, 2012 [PDF]

• Optimization of inverse Snyder polyhedral projection, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, International Conference on Cyberworlds (CW), in association with ACM SIGGRAPH and Eurographics, IEEE Computer Society, pp. 136-143 (Oct 2011) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

Related papers

• One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%
• Analysis of inverse Snyder optimizations, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, Transactions on Computational Science XVI, LNCS 7380, Springer Berlin Heidelberg, pp. 134-148 (2012) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%
• Optimization of inverse Snyder polyhedral projection, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, International Conference on Cyberworlds (CW), in association with ACM SIGGRAPH and Eurographics, IEEE Computer Society, pp. 136-143 (Oct 2011) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%%

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/inv-snyder-cw2011-harrison.png

MSc Thesis

• Equal Area Spherical Subdivision, Erika Harrison, 2012 [PDF]

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/inv-snyder-tcs2012-harrison.png

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/inv-snyder-cw2011-harrison.png

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/1-to-2-de-isvc2013-mahdavi-amiri.png

• One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

• Analysis of inverse Snyder optimizations, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, Transactions on Computational Science XVI, LNCS 7380, Springer Berlin Heidelberg, pp. 134-148 (2012) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

• Optimization of inverse Snyder polyhedral projection, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, International Conference on Cyberworlds (CW), in association with ACM SIGGRAPH and Eurographics, IEEE Computer Society, pp. 136-143 (Oct 2011) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=18px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

• One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=20px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=17px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/1-to-2-de-isvc2013-mahdavi-amiri.png

• Analysis of inverse Snyder optimizations, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, Transactions on Computational Science XVI, LNCS 7380, Springer Berlin Heidelberg, pp. 134-148 (2012) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=40px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=35px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/inv-snyder-tcs2012-harrison.png

• Optimization of inverse Snyder polyhedral projection, Erika Harrison, Ali Mahdavi-Amiri, and Faramarz Samavati, International Conference on Cyberworlds (CW), in association with ACM SIGGRAPH and Eurographics, IEEE Computer Society, pp. 136-143 (Oct 2011) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=40px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=35px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/inv-snyder-cw2011-harrison.png

• One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013) http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=40px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=35px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

Related papers

• One-to-two digital earth, Ali Mahdavi-Amiri, Faraz Bhojani, and Faramarz Samavati, Advances in Visual Computing - ISVC 2013, LNCS 8034, Springer Berlin Heidelberg, pp. 681-692 (Jul 2013)
  
  http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/publishericon.png%% %width=40px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/pdficon.png%% %width=35px%http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/bibtexicon.png%%

http://jungle.cpsc.ucalgary.ca/wiki/uploads/Publications-FS/1-to-2-de-isvc2013-mahdavi-amiri.png

When you take a picture you are performing a projection from three dimensions (the world) down to two dimensions (a flat photograph). While camera perform one type of projection, different lenses (e.g., fisheye lenses) and photographic methods (panorama stitching) create different types of projections.

However, there are a wide variety of other projections that cannot be taken with a camera. For instance, the orthographic projections used to create blue prints. In paintings artists take this even further exploring entirely different representations of space.

http://pages.cpsc.ucalgary.ca/~brosz/foo/otherprojections.jpg

Flexible projection is a project that aims make a wider variety of projection possible within computer graphics environments. One of the main concepts in this work is to employ modeling techniques and interfaces to organize the flattening of a volume into a 2D plane. Flexible Projection not only provides a means for including nonstandard projections in graphics systems but also provides a consistent means of creating and working with a wide variety of different projections.

http://pages.cpsc.ucalgary.ca/~brosz/research/projection/figs/kiasetup.png http://pages.cpsc.ucalgary.ca/~brosz/research/projection/figs/kia.png

Flexible Projection explicitly model the 3D volume as a parametric volume. Beginning with a cube one can flexibly adjust this volume into other shapes: a frustum for perspective, a cylinder for a cylindrical panorama, a hemisphere for a fisheye thus allowing for a diverse variety of projections. This relation between the volume's shape and the resulting projection creates a link that can assist in visual communication of the projection's behaviour without resorting to mathematical equations.

We have explored several different applications for Flexible Projections:

http://pages.cpsc.ucalgary.ca/~brosz/research/panorama/cylinder.png %width=300px%http://pages.cpsc.ucalgary.ca/~brosz/research/panorama/cylinderwindow.png Altering Panoramas

http://pages.cpsc.ucalgary.ca/~brosz/foo/vangoghrecreation.jpg Reproducing (A1, A2) & Re-applying Van Gogh's Projection (B)

http://pages.cpsc.ucalgary.ca/~brosz/foo/alteringprojection.jpg Altering Projections

Downloads

• A demo video from an early version of this work avi video
  
  

Related papers

• Single Camera Flexible Projection, J. Brosz, F.F. Samavati, S. Carpendale, M.C. Sousa. Proceedings of the 4th International Symposium on Non-Photorealistic Animation and Rendering (NPAR 2007). [PDF]
• Art and Nonlinear Projection, J. Brosz, S. Carpendale, F.F. Samavati, H. Wang, A. Dunning. Proceedings of Bridges 2009: Mathematical Connections in Art, Music, and Science. [PDF]
• Shape Defined Panoramas, J. Brosz and F.F. Samavati. Proceedings of the 8th Eurographics/ACM Symposium on Sketch-Based Interfaces and Modeling (SBIM'11), Aix-en-Provence, France, 2011. [PDF]

PhD Thesis

• The Flexible Projection Framework. John Brosz, 2011 [PDF]