Background. Rasterization of triangle geometry has been the dominating rendering technique in the real-time rendering industry for many years. However, triangles are not always easy to work with for content creators. With the introduction of hardware-accelerated ray tracing, rasterization-based lighting techniques have been steadily replaced by ray tracing techniques. This shift may signify the opportunity of exploring other, more easily manipulated, geometry-type alternatives compared to triangle geometry. One such geometry type is implicit surfaces. Objectives. This thesis investigates the rendering speed, editing speed, and image quality of different implicit surface rendering techniques using a state-of-the-art, hardware-accelerated, path tracing implementation. Furthermore, it investigates how implicit surfaces may be edited in real time and how editing affects rendering. Methods. A baseline direct sphere tracing algorithm is implemented to render implicit surfaces. Additionally, dense and narrow band discretization algorithms that sphere trace a discretization of the implicit surface are implemented. For each technique, two variations that provide potential benefits in rendering speed are also tested. Additionally, a real-time implicit surface editor that can utilize all the mentioned rendering techniques is created. Rendering speed, editing speed, and image quality metrics are captured for all techniques using different scenes created with the editor and an existing hardware-accelerated path tracing solution. Image quality differences are measured using mean squared error and the image difference evaluator FLIP. Results. Direct sphere tracing achieves the best image quality results but has the slowest rendering speed. Dense discretization achieves the best rendering speed in most tests and achieves better image quality results compared to narrow band discretization. Narrow band discretization achieves significantly better editing speed than both direct sphere tracing and dense discretization. All variations of each algorithm achieve better or equal rendering and editing speed compared to their standard implementation. All algorithms achieve real-time rendering and editing performance. However, only discretized methods display real-time rendering performance for all scenes, and only narrow band discretization displays real-time editing performance for a larger number of primitives. Conclusions. Implicit surfaces can be rendered and edited in real time while using a state-of-the-art, hardware-accelerated, path tracing algorithm. Direct sphere tracing degrades in performance when the implicit surface has an increased number of primitives, whereas discretization techniques perform independently of this. Furthermore, narrow band discretization is fast enough so that editing can be performed in real time even for implicit surfaces with a large number of primitives, which is not the case for direct sphere tracing or dense discretization. / Bakgrund. Triangelrastrering har varit den dominerande renderingstekniken inom realtidsgrafik i flera år. Trianglar är dock inte alltid lätta att jobba med för skapare av grafiska modeller. Med introduktionen av hårdvaruaccelererad strålspårning har rastreringsbaserade ljussättningstekniker stadigt ersatts av strålspårningstekniker. Detta skifte innebär att det kan finnas möjlighet för att utforska andra, mer lättredigerade geometrityper jämfört med triangelgeometri, exempelvis implicita ytor. Syfte. Detta examensarbete undersöker rendering- och redigeringshastigheten, samt bildkvaliteten av olika renderingstekniker för implicita ytor tillsammans med en spjutspetsalgoritm för hårdvaruaccelererad strålföljning. Den undersöker även hur implicita ytor kan redigeras i realtid och hur det påverkar rendering. Metod. En direkt sfärspårningsalgoritm implementeras som baslinje för att rendera implicita ytor. Även algoritmer som utför sfärstrålning över en kompakt- och smalbandsdiskretisering av den implicita ytan implementeras. För varje teknik implementeras även två variationer som potentiellt kan ge bättre prestanda. Utöver dessa renderingstekniker skapas även ett redigeringsverktyg för implicita ytor. Renderingshastighet, redigeringshastighet, och bildkvalité mäts för alla tekniker över flera olika scener som har skapats med redigeringsverktyget tillsammans med en hårdvaruaccelererad strålföljningsalgoritm. Skillnader i bildkvalité utvärderas med hjälp av mean squared error och evalueringsverktyget för bildskillnader som heter FLIP. Resultat. Direkt sfärspårning åstadkommer bäst bildkvalité, men har den långsammaste renderingshastigheten. Kompakt diskretisering renderar snabbast i de flesta tester och åstadkommer bättre bildkvalité än vad smalbandsdiskretisering gör. Smalbandsdiskretisering åstadkommer betydligt bättre redigeringshastighet än både direkt sfärspårning och kompakt diskretisering. Variationerna för respektive algoritm presterar alla lika bra eller bättre än standardvarianten för respektive algoritm. Alla algoritmer uppnår realtidsprestanda inom rendering och redigering. Endast diskretiseringsmetoderna uppnår dock realtidsprestanda för rendering med alla scener och endast smalbandsdiskretisering uppnår realtidsprestanda för redigering med ett större antal primitiver. Slutsatser. Implicita ytor kan renderas och redigeras i realtid tillsammans med en spjutspetsalgoritm för hårdvaruaccelererad strålföljning. Vid användning av direkt sfärstrålning minskar renderingshastigheten när den ytan består av ett stort antal primitiver. Diskretiseringstekniker har dock en renderingshastighet som är oberoende av antalet primitiver. Smalbandsdiskretisering är tillräckligt snabb för att redigering ska kunna ske i realtid även för implicita ytor som består stora antal primitiver.

Les matériaux discrets entrecroisés (DIM) rigides sont une classe de matériaux qui se distinguent par la manière unique par laquelle ils se déforment: les DIMs sont composés d’éléments (connectés par entrecroisements) qui peuvent se déplacer librement à l’intérieur d’une amplitude définie par les contacts avec leurs éléments voisins. Ceci donne une réponse biphasique aux déformations unique à ces structures où soit aucune résistance n’est fournie à une déformation, soit un arrêt complet à la déformation se présente. Il n’est pas clair comment l’ensemble de paramètres discrets et continus décrivant un DIM influence ce comportement biphasique. De plus, nous ne possédons pas les outils pour le charactériser correctement. Dans le but d’élucider ce comportement, nous présentons une méthode qui s’inspire de techniques d’homogénisation qui peut détecter les contacts physiques entre éléments composés de tores. En définissant une énergie adéquate, nous pouvons minimiser les intersections entre éléments tout en déformant le DIM d’une façon arbitraire en utilisant des techniques d’optimisation standardes. Nous explorons les déformations auxquelles des arrangements planaires de DIMs peuvent être assujettis et investiguons comment le couplage de contraintes dans deux directions orthogonales influence ces déformations. Nos résultats permettent de mieux comprendre comment différents paramètres décrivant un DIM influence ces déformations. / Rigid discrete interlocking materials (DIMs) are a class of materials that distinguish themselves by the unique way in which they deform: in DIMs, elements (connected through interlocking) can move freely within a range defined through contacts with neighbouring elements. This results in a biphasic deformation behaviour unique to these structures where no resistance is provided to deformation or a hard stop to deformation is met. It is yet unclear how the set of discrete and continuous parameters describing a DIM influences this biphasic behaviour. Likewise, we lack tools to properly characterize it. To that effect, we present a method which takes inspiration from homogenization and handles contacts by leveraging the definition of implicit surfaces, specifically tori, making up our elements. By defining an adequate energy function, we can minimize intersection between elements while deforming the DIM in an arbitrary way using standard optimization approaches. We explore the deformations that planar sheets of DIM can be subjected to and investigate how the coupling of constraints in two orthogonal directions affects these deformations. Our results give insights on how the tuning of various parameters describing the DIM affects these deformations.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-06T13:51:44Z No. of bitstreams: 1 THICIANY MATSUDO IWANO - DISSERTAÇÃO PPGMAT 2005..pdf: 3751075 bytes, checksum: 2aaae3fdd115cd9f6f4b653f522d94c8 (MD5) / Made available in DSpace on 2018-07-06T13:51:44Z (GMT). No. of bitstreams: 1 THICIANY MATSUDO IWANO - DISSERTAÇÃO PPGMAT 2005..pdf: 3751075 bytes, checksum: 2aaae3fdd115cd9f6f4b653f522d94c8 (MD5) Previous issue date: 2005-10 / Neste trabalho apresentamos um estudo das principais técnicas de geração de malhas poligonais, a partir de superfícies descritas matematicamente por funções implícitas,isto é, superfícies definidas pelo conjunto S = f−1(0) = {X ∈ R3 | f(X) = 0}, onde f : R3 → R e f é, pelo menos, de classe C2. Mostramos um método para obter as curvaturas gaussiana e média dessas superfícies a partir do vetor ∇f para cada ponto de S. Abordamos questões como a preservação de características geométricas e topológicas do objeto gráfico. Dentre os métodos estudados, ressaltamos o algoritmo Marching Triangles, que gera uma malha a partir de um ponto arbitrário p sobre a superfície S e um referencial local, usando a abordagem do avanço de frentes. Em sua implementação, usamos o raio de curvatura, calculado a partir da curvatura normal máxima absoluta da superfície em cada ponto p pertencente a S, para adaptar o comprimento das arestas da malha triangular à geometria local da superfície S / In this work we present a study about the main techniques of surfaces meshes generation, described by implicit functions, that is, surfaces defined by the set S = f−1(0) = {X ∈ R3 | f(X) = 0}, where f : R3 → R and f is, at least, C2. We discuss aspects involving his preservation of graphic object’s geometry and topology. As special method we cite the Marching Triangles that generates a mesh starting from an arbitrary point p on surface S and a local referencial, using advancing fronts approach. In our implementation, we use the radius of curvature, calculated from surface’s absolute maximum normal curvature in each point p in S and the triangular mesh, to adapt the edges length of the mesh to the local geometry.