POV-Ray - The Persistence of Vision Raytracer Implicit surface Implicit surface torus (R=40, a=15). Implicit surface of genus 2. Implicit non-algebraic surface (wineglass). An implicit surface is the set of zeros of a function of three variables. The graph of a function is usually described by an equation and is called an explicit representation. , where the x-, y- and z-coordinates of surface points are represented by three functions depending on common parameters . is given: (implicit), (parametric). Examples: For a plane, a sphere, and a torus there exist simple parametric representations. The implicit function theorem describes conditions under which an equation can be solved (at least implicitly) for x, y or z. If is polynomial in x, y and z, the surface is called algebraic. Despite difficulty of visualization, implicit surfaces provide relatively simple techniques to generate theoretically (e.g. Formulas[edit] Throughout the following considerations the implicit surface is represented by an equation where function are Tangent plane and normal vector[edit] at
DGPF - Deutsche Gesellschaft für Photogrammetrie, Fernerkundung und Geoinformation e.V. - Home Isosurface Surface representing points of constant value within a volume The term isoline is also sometimes used for domains of more than 3 dimensions.[1] Applications[edit] Isosurfaces are normally displayed using computer graphics, and are used as data visualization methods in computational fluid dynamics (CFD), allowing engineers to study features of a fluid flow (gas or liquid) around objects, such as aircraft wings. Numerous other disciplines that are interested in three-dimensional data often use isosurfaces to obtain information about pharmacology, chemistry, geophysics and meteorology. Implementation algorithms[edit] Marching cubes[edit] Asymptotic decider[edit] The asymptotic decider algorithm was developed as an extension to marching cubes in order to resolve the possibility of ambiguity in it. Marching tetrahedra[edit] The marching tetrahedra algorithm was developed as an extension to marching cubes in order to solve an ambiguity in that algorithm and to create higher quality output surface.
Defining generative design and its software implementation with nTopology, Frustum, and ParaMatters Breaking announcements in printable materials, hardware, and the latest end-use applications are now standard at major 3D printing conferences. Focusing on the latest parts designed for additive manufacturing, typical explanations for how each was conceived likely include the terms topology optimization, lattice design, and generative design. Although these concepts are well established in an academic sense, their commercial implementation and technical definitions have become the focus of large corporations and startups alike. Driven by greater part manufacturing freedom and a need for efficient generation of optimized designs, the design software world is rising to the challenge with software innovations across CAD, CAM, and CAE applications. nTopology, Frustum, and ParaMatters are three venture-backed startups that are pushing to redefine how parts are designed optimally and efficiently for any manufacturing method. The definition of generative design Looking forward
FreeWRL/FreeX3D Home Page Visualisation 3D d’une fonction réelle de deux variables (de ℝ² dans ℝ) avec Python -matplotlib | by Joséphine Picot | Medium PS : Si vous avez déjà suivi le tutoriel “Visualisation des cercles de niveau d’une fonction réelle”, vous pouvez passer directement à la partie “Visualisation” de ce tutoriel car la préparation des données est la même. Tout d’abord quelques librairies sont nécessaires : installation pip install numpypip install matplotlib importation import numpy as npimport matplotlib.pyplot as pltimport mpl_toolkitsfrom mpl_toolkits.mplot3d import Axes3D Si vous avez une erreur lors de l’importation de mpl_toolkit, essayez d’exécuter la commande suivante : ! Étapes de préparation Soit une fonction f de ℝ² dans ℝ. f(x, y) = 2*x² — x*y + 2*y² On définit la fonction f en python : def f(x, y): return 2*x**2 - x*y + 2*y**2 On choisit un intervalle de valeurs dans l’ensemble des réels ℝ pour x et y (je prendrai pour exemple [-100, 100] avec 100 valeurs pour chaque variable). x = np.linspace(-100, 100, 100)y = np.linspace(-100, 100, 100) X, Y = np.meshgrid(x, y) Z = f(X,Y) Visualisation interactive %matplotlib notebook
Polygonising a scalar field (Marching Cubes) Also known as: "3D Contouring", "Marching Cubes", "Surface Reconstruction" Written by Paul Bourke May 1994 Based on tables by Cory Gene Bloyd along with additional example source code marchingsource.cppAn alternative table by Geoffrey Heller.rchandra.zip: C++ classes contributed by Raghavendra Chandrashekara.OpenGL source code, sample volume: cell.gz (old)volexample.zip: An example showing how to call polygonise including a sample MRI dataset.Improved (2018) Qt/OpenGL example courtesy Dr. This document describes an algorithm for creating a polygonal surface representation of an isosurface of a 3D scalar field. There are many applications for this type of technique, two very common ones are: Reconstruction of a surface from medical volumetric datasets. The fundamental problem is to form a facet approximation to an isosurface through a scalar field sampled on a rectangular 3D grid. The indexing convention for vertices and edges used in the algorithm are shown below Another example Source code
3D Printing Introduction 3D printers 3D printing explained A 3D print starts off as a virtual design of the object to be printed. Methods of 3D printing Not every printer used the same technology to construct its prints, several ways of building a print exist and all of those technologies as of 2012 are additive. SLS (Selective Laser Sintering) Wiki website This technology uses a high powered laser to fuse powder made up of plastic, metal, ceramic or glass granulate to create the model. FDM (Fused Deposition Modeling) Fused deposition modeling works by using a plastic filament or metal wire to feed an extruder. SLA (Stereolithography) The technique of stereolithography uses a UV-laser to cure layers of UV-curable photopolymer resin to create layers of the object. Model creation When designing an object for 3D printing, a program used for 3D modeling is used to generate the geometry of the design. Creating a model is possible in a wide variety of CAD programs, in this case we will focus on Rhinoceros. Links
Main Page - Crystal Space 3D Direction Fields - Geometry Central This section describes routines for computing n-direction fields on a surface. An n-direction field on a surface assigns n evenly-spaced unit tangent vectors to each point on the surface. For example, a 1-direction field is an ordinary direction field, a 2-direction field is a line field, and a 4-direction field is a cross field. Most of these routines only depend on the intrinsic geometry of a surface (via the IntrinsicGeometryInterface). Therefore, you can run them on abstract geometric domains as well as traditional surfaces in 3D. #include "geometrycentral/surface/direction_fields.h" Smoothest Direction Fields These routines compute the smoothest possible n-direction field on the input surface. The two routines are almost identical. Example Smoothest Boundary-Aligned Direction Fields This routine works like the previous ones, except it imposes Dirichlet boundary conditions to force the generated direction field to be aligned with the mesh’s boundary. Curvature-Aligned Direction Fields