Complex 3D digital objects are used in many domains such as animation films, scientific visualization, medical imaging and computer vision. These objects are usually represented by triangular meshes with many triangles. The simplification of those objects in order to keep them as close as possible to the original has received a lot of attention in the recent years. In this context, we propose a simplification algorithm which is focused on the accuracy of the simplifications. The mesh simplification uses edges collapses with vertex relocation by minimizing an error metric. Accuracy is obtained with the two error metrics we use: the Accurate Measure of Quadratic Error (AMQE) and the Symmetric Measure of Quadratic Error (SMQE). AMQE is computed as the weighted sum of squared distances between the simplified mesh and the original one. Accuracy of the measure of the geometric deviation introduced in the mesh by an edge collapse is given by the distances between surfaces. The distances are computed in between sample points of the simplified mesh and the faces of the original one. SMQE is similar to the AMQE method but computed in the both, direct and reverse directions, i.e. simplified to original and original to simplified meshes. The SMQE approach is computationnaly more expensive than the AMQE but the advantage of computing the AMQE in a reverse fashion results in the preservation of boundaries, sharp features and isolated regions of the mesh. For both measures we obtain better results than methods proposed in the literature.

Present graphic requires a lot of optimizations of rendering techniques and mathematical calculations. It is caused by increased requirements of scene's visualization. One of scene's optimizing techniques is the Level of detail. This thesis is focused on methods used by LOD in OpenSceneGraph and OpenGL library. Next it will be described how to choose the right level of detail in a scene. Later it will be explained how to simplify 3D models. These techniques will be implemented in converting tool and demonstrating application. Methods for simplify 3D models will be tested for their speed and quality.

Les objets numériques 3D sont utilisés dans de nombreux domaines, les films d'animations, la visualisation scientifique, l'imagerie médicale, la vision par ordinateur.... Ces objets sont généralement représentés par des maillages à faces triangulaires avec un nombre énorme de triangles. La simplification de ces objets, avec préservation de la géométrie originale, a fait l'objet de nombreux travaux durant ces dernières années. Dans cette thèse, nous proposons un algorithme de simplification qui permet l'obtention d'objets simplifiés de grande précision. Nous utilisons des fusions de couples de sommets avec une relocalisation du sommet résultant qui minimise une métrique d'erreur. Nous utilisons deux types de mesures quadratiques de l'erreur : l'une uniquement entre l'objet simplifié et l'objet original (Accurate Measure of Quadratic Error (AMQE) ) et l'autre prend aussi en compte l'erreur entre l'objet original et l'objet simplifié ((Symmetric Measure of Quadratic Error (SMQE)) . Le coût calculatoire est plus important pour la seconde mesure mais elle permet une préservation des arêtes vives et des régions isolées de l'objet original par l'algorithme de simplification. Les deux mesures conduisent à des objets simplifiés plus fidèles aux originaux que les méthodes actuelles de la littérature. / Complex 3D digital objects are used in many domains such as animation films, scientific visualization, medical imaging and computer vision. These objects are usually represented by triangular meshes with many triangles. The simplification of those objects in order to keep them as close as possible to the original has received a lot of attention in the recent years. In this context, we propose a simplification algorithm which is focused on the accuracy of the simplifications. The mesh simplification uses edges collapses with vertex relocation by minimizing an error metric. Accuracy is obtained with the two error metrics we use: the Accurate Measure of Quadratic Error (AMQE) and the Symmetric Measure of Quadratic Error (SMQE). AMQE is computed as the weighted sum of squared distances between the simplified mesh and the original one. Accuracy of the measure of the geometric deviation introduced in the mesh by an edge collapse is given by the distances between surfaces. The distances are computed in between sample points of the simplified mesh and the faces of the original one. SMQE is similar to the AMQE method but computed in the both, direct and reverse directions, i.e. simplified to original and original to simplified meshes. The SMQE approach is computationnaly more expensive than the AMQE but the advantage of computing the AMQE in a reverse fashion results in the preservation of boundaries, sharp features and isolated regions of the mesh. For both measures we obtain better results than methods proposed in the literature.

VYSOKÉ UČENÍ TECHNICKÉ V BRNĚ The purpose of this work is to design and implement a computer system, which should be used for simplification of a polygonal models in 3D space. The system should be allowed to reduce a given number of geometrical primitives from source object. User should have impact to the reducing process by selecting a method, size of target object etc. System uses 3DS file format for model loading and saving. Reader should understand principles of the polygon reduction and used algorithms.