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Fast RayAxis Aligned Bounding Box Overlap Tests with Plucker Coordinates
 Journal of Graphics Tools
"... Fast rayaxis aligned bounding box overlap tests can be performed by utilizing Plücker coordinates. This method tests the ray against the edges comprising the silhouette of the box instead of testing against individual faces. Projection of the edges onto a 2D plane to generate the silhouette is no ..."
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Fast rayaxis aligned bounding box overlap tests can be performed by utilizing Plücker coordinates. This method tests the ray against the edges comprising the silhouette of the box instead of testing against individual faces. Projection of the edges onto a 2D plane to generate the silhouette is not necessary, which simplifies the technique. The method is divisionfree and successive calculations are independent and consist simply of dot product operations, which permits vectorization. The method does not compute an intersection distance along the ray to the box, but this can be added as an additional step. Test results show the technique’s performance is up to 87 % faster than traditional methods if an intersection distance is not needed. Sample source code is available online.
A tutorial on SE(3) transformation parameterizations and onmanifold optimization
"... An arbitrary rigid transformation in SE(3) can be separated into two parts, namely, a translation and a rigid rotation. This technical report reviews, under a unifying viewpoint, three common alternatives to representing the rotation part: sets of three (yawpitchroll) Euler angles, orthogonal rota ..."
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An arbitrary rigid transformation in SE(3) can be separated into two parts, namely, a translation and a rigid rotation. This technical report reviews, under a unifying viewpoint, three common alternatives to representing the rotation part: sets of three (yawpitchroll) Euler angles, orthogonal rotation matrices from SO(3) and quaternions. It will be described: (i) the equivalence between these representations
and the formulas for transforming one to each other (in all cases considering the translational and rotational parts as a whole), (ii) how to compose poses with poses and poses with points in each representation and (iii) how the uncertainty of the poses (when modeled as Gaussian distributions) is affected by these transformations and compositions. Some brief notes are also given about the
Jacobians required to implement leastsquares optimization on manifolds, an very promising approach in recent engineering literature. The text reﬂects which MRPT C++ library functions implement each of the described algorithms. All the implementations have been thoroughly validated by means of unit testing and numerical estimation of the Jacobians.
Sense and sidedness in the graphics pipeline via a passage through a separable space
 THE VISUAL COMPUTER
, 2009
"... Computer graphics is ostensibly based on projective geometry. The graphics pipeline—the sequence of functions applied to 3D geometric primitives to determine a 2D image—is described in the graphics literature as taking the primitives from Euclidean to projective space, and then back to Euclidean spa ..."
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Computer graphics is ostensibly based on projective geometry. The graphics pipeline—the sequence of functions applied to 3D geometric primitives to determine a 2D image—is described in the graphics literature as taking the primitives from Euclidean to projective space, and then back to Euclidean space. This is a weak foundation for computer graphics. An instructor is at a loss: one day entering the classroom and invoking the established and venerable theory of projective geometry while asserting that projective spaces are not separable, and then entering the classroom the following week to tell the students that the standard graphics pipeline performs clipping not in Euclidean, but in projective space—precisely the operation (deciding sidedness, which depends on separability) that was deemed nonsensical. But there is no need to present Blinn and Newell’s algorithm [4, 24]—the crucial clipping step in the graphics pipeline and, perhaps, the most original knowledge a student learns in a fourthyear computer graphics class—as a clever trick that just works. Jorge Stolfi described in 1991 oriented projective geometry. By declaring the two vectors (x, y, z, w) T and (−x, −y, −z, −w) T distinct, Blinn and Newell were already unknowingly working in oriented projective space. This paper presents the graphics pipeline on this stronger foundation.
LIBRARY FOR COMPUTATION IN THE PROJECTIVE SPACE
"... Abstract. The paper describes a library for computation in the projective space developed for use within C # and.NET environment. This experimental library is used to prove that computation in projective space can lead to elimination of the division operation in many cases and therefore to more robu ..."
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Abstract. The paper describes a library for computation in the projective space developed for use within C # and.NET environment. This experimental library is used to prove that computation in projective space can lead to elimination of the division operation in many cases and therefore to more robust algorithms. The taken approach unfortunately requires a change of the architecture of the current CPUs, nevertheless there is a hope that the proposed approach is reasonable.
An Implicit Surface based 2D / 3D Medial Extractor
, 2003
"... dedicated with gratitude to My mother, father and guruji brahmashri siddharajan swamigal ..."
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dedicated with gratitude to My mother, father and guruji brahmashri siddharajan swamigal
Acknowledgments
, 2005
"... This thesis is dedicated to my family. ii The objective of this work is to unify an imagecentric 2D view of the world and a visioncentric 3D view of the world in the context of inbetweening/view interpolation. This is achieved by incorporating epipolar geometry into an existing inbetweening algo ..."
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This thesis is dedicated to my family. ii The objective of this work is to unify an imagecentric 2D view of the world and a visioncentric 3D view of the world in the context of inbetweening/view interpolation. This is achieved by incorporating epipolar geometry into an existing inbetweening algorithm [8], which is built on a Bayesian framework. Issues include estimation of the fundamental matrix, specification of the new view and how to incorporate the geometry. The resulting hybrid algorithm exploits the geometry by inserting an additional prior, an epipolar constraint prior, into the existing Bayesian framework. When this hybrid algorithm is used to produce new views, the improvement is manifested in better treatment of occlusion. It is expected that, through improving the accuracy of the new view specification and through more experiments in exploitation of the geometry, further improvements could be achieved. Declaration I hereby declare that this thesis has not been submitted as an exercise for a degree at this or any other University and that it is entirely my own work, except where otherwise accredited. I agree that the Library may lend or copy this thesis upon request.
Todd Dinner Precision Rehab Manufacturing Inc.
"... Abstract — This paper presents a systematic approach to construct a gridbased 3D surface model for a customized cushion seat for people with disabilities. Initially, a 2D grid map is defined as the bottom surface of the cushion seat based on the required resolution. Then each point in the 2D grid m ..."
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Abstract — This paper presents a systematic approach to construct a gridbased 3D surface model for a customized cushion seat for people with disabilities. Initially, a 2D grid map is defined as the bottom surface of the cushion seat based on the required resolution. Then each point in the 2D grid map is projected onto one surface point in the 3D pixelbased point cloud. The height of each surface point is approximated using the nearest neighbor algorithm. A tool box is developed for the visualization the constructed 3D surface model. The height of the 3D surface computed using this tool box is compared with the manually designed cushion seat at Precision Rehab Manufacturing Inc. and found to be within tolerance. Keywords stereo camera, gridbased 3D surface model, pixelbased point cloud, customized seat I.