Convolution filtering of continuous signed distance fields for polygonal meshes

Signed distance fields obtained from polygonal meshes are commonly used in various applications. However, they can have C1 discontinuities causing creases to appear when applying operations such as blending or metamorphosis. The focus of this work is to efficiently evaluate the signed distance function and to apply a smoothing filter to it while preserving the shape of the initial mesh. The resulting function is smooth almost everywhere, while preserving the exact shape of the polygonal mesh. Due to its low complexity, the proposed filtering technique remains fast compared to its main alternatives providing C1-continuous distance field approximation. Several applications are presented such as blending, metamorphosis and heterogeneous modelling with polygonal meshes

Automatic and topology-preserving gradient mesh generation for image vectorization

Demonska vjera polazi od toga da se ne nalazi isključivo u nevjeri, nego je ona onkraj nevjere. Ovim radom smo prvo željeli prikazati glavne postavke najbitnijih elemenata teologalne vjere da bismo kasnije kroz filozofske teze F. Hadjadja prikazali glavna obilježja vjere zlih demona koja su duhovnog karaktera i predstavljaju veliku opasnost za čovjeka i njegovu vjeru. Unatoč različitim tumačenjima, Hadjadj želi upozoriti na to da se zli demoni ne nalaze samo među ateistima, agnosticima i ostalim pokretima koji, na neki način, niječu Božu opstojnost, nego ti zli demoni zapravo vjeruju, pa zato za polazište uzima redak iz Jakovljeve poslanice u kojoj piše da oni „vjeruju i dršću”. Na kraju smo ovim radom prikazali važnost sinteze duše i tijela, odnosno utjelovljenja u kršćanstvu jer je misterij katoličke vjere misterij utjelovljenja i nemoguće je odbacivati tjelesnost kao što je to slučaj u različitim spiritualističkim dimenzijama.Demonic faith is not strictly associated with infidelity itself, but rather exists beyond it. This work aims to present the main postulates of the most crucial elements of the theological faith in order to show, using F. Hadjadj's philosophical thesis, the main characteristics associated with evil demons, which are of the spiritual nature and present great danger for man and his faith. Despite various interpretations, Hadjadj wishes to point out that evil demons do not dwel lonly within atheists, agnostics and other movements which, in a way, negate the existence of God, but that these evil demons actually do believe, and therefore he uses as a starting point the line from the Epistle of Jacob that states that demons „believe and tremble”. In the end, this work presented the importance of the body-soul synthesis, which is the incarnation in Christianity, since the mistery of the Catholic faith is the mistery of the incarnation, and it is impossible to discard corporeality, which is the case in various spiritual dimensions

Differentiable Subdivision Surface Fitting

In this paper, we present a powerful differentiable surface fitting technique to derive a compact surface representation for a given dense point cloud or mesh, with application in the domains of graphics and CAD/CAM. We have chosen the Loop subdivision surface, which in the limit yields the smooth surface underlying the point cloud, and can handle complex surface topology better than other popular compact representations, such as NURBS. The principal idea is to fit the Loop subdivision surface not directly to the point cloud, but to the IMLS (implicit moving least squares) surface defined over the point cloud. As both Loop subdivision and IMLS have analytical expressions, we are able to formulate the problem as an unconstrained minimization problem of a completely differentiable function that can be solved with standard numerical solvers. Differentiability enables us to integrate the subdivision surface into any deep learning method for point clouds or meshes. We demonstrate the versatility and potential of this approach by using it in conjunction with a differentiable renderer to robustly reconstruct compact surface representations of spatial-temporal sequences of dense meshes