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Topic: Implicit surface

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	Variational Implicit Surfaces (Site not responding. Last check: 2007-11-06)
		An implicit surface is quite different from a parametric surface.
		Whereas a parametric surface, such as a cubic patch or a polygonal mesh, has specific surface coordinates, implicit surfaces allow no such surface navigation.
		However, an implicit surface is fully aware of its interior and exterior, making it an ideal candidate for shape transformation, collision detection, CSG, and blending.
	www.gvu.gatech.edu /geometry/implicit/varimp.html (317 words)

	Basic Concepts
		Therefore, spheres and all quadric surfaces are algebraic surfaces of degree two, while torus is a degree four algebraic surface.
		For implicit surfaces, however, situation is different because we do not have a domain to triangulate.
		The left surface is a hyperbolic paraboloid and the right one is a ring Dupin cyclide which is a degree 4 rational surface.
	www.cs.mtu.edu /~shene/COURSES/cs3621/NOTES/surface/basic.html (1555 words)

	Modelling with Implicit Surfaces that Interpolate (Site not responding. Last check: 2007-11-06)
		These implicit surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface.
		A 3D implicit function is created from these constraints using a variational scattered data interpolation approach, and the iso-surface of this function describes a surface.
		Like other implicit surface descriptions, these surfaces can be used for CSG and interference detection, may be interactively manipulated, are readily approximated by polygonal tilings, and are easy to ray trace.
	www.cc.gatech.edu /~turk/vimp/index.html (266 words)

	Dr. Dobb's \| Implicit Surfaces and Real-Time Graphics \| July 22, 2001
		Implicit surfaces are generally defined by an equation model that provides a logical basis for creating a closed surface in space.
		Implicit surfaces are useful in that they can be used in areas such as molecular modeling, animation, geophysical systems, and weather analysis.
		Implicit surfaces can be generated in many different ways, the most common being to design an equation that models the desired surface, then visualize or model it.
	www.ddj.com /184410227 (2783 words)

	Surface - Wikipedia, the free encyclopedia
		The expression thus derived from a fundamental polygon of a surface turns out to be the sole relation in a presentation of the fundamental group of the surface with the polygon edge labels as generators.
		Smooth surfaces equipped with Riemannian metrics are of foundational importance in differential geometry.
		Minimal surfaces are surfaces that minimize the surface area for given boundary conditions.
	en.wikipedia.org /wiki/Surface (1585 words)

	CVSSP 3DVision: Introduction to Model Building from 3D Surface Measurements
		An implicit surface representation is then constructed based on the zero-set of a signed field function which is the distance to the nearest point on the surface.
		Marching cubes implicit surface polygonisation is then used to generate a single triangulated mesh model of the object surface.
		The surface of the object is then scanned and regions close to surface label as seen, regions between the sensor and surface as empty and all other regions as unseen.
	www.ee.surrey.ac.uk /Research/VSSP/3DVision/model_building/model.html (4016 words)

	Implicit surfaces
		The question as to whether points are on the interior or exterior of the surface is implicit to the description.
		Implicit surfaces can most readily be viewed in traditional rendering packages by polygonisation with for example the marching cubes algorithm.
		People have known for a long time that if you have two implicit surfaces f(x,y,z)=0 and g(x,y,z)=0 that are fairly continuous, with a common sign convention (f and g positive on the inside, negative on the outside, say) then the implicit surface defined by f+g=0 is a blend of the shapes.
	local.wasp.uwa.edu.au /~pbourke/modelling/implicitsurf (1143 words)

	Contouring Implicit Surfaces
		To render an implicit surface this way, however, it is first required to compute the polygonal approximation of its contour.
		The Marching Cubes algorithm, published in 1987 [4], laid the foundation for the extraction of a polygonal approximation of an implicit surface.
		In the context of an implicit surface, the normal vector of some point (x,y,z) in the volume can be approximated as the gradient of the field function in each of the three axes x, y, z.
	www.geocities.com /tzukkers/isosurf/isosurfaces.html (5375 words)

	Graphics and Visualization (Site not responding. Last check: 2007-11-06)
		Implicit surfaces are shapes described by the points where a function is zero.
		Sphere tracing is a recently developed method for rendering implicit surfaces that operates on implicit functions that indicate the distance to the implicit surface.
		It ray traces implicit surfaces by tracking along each ray by the distance to the implicit surface, as reported by the implicit function.
	www.eecs.wsu.edu /~irl/summary/graphics.html (710 words)

	Advanced Surface Library: Implicit class Reference
		This class is typically invoked as "Implicit f" where f is a pointer to some instance of a concrete subclass of Implicit*.
		In this implementation, we define the value of the function to be negative "within" an implicit surface, 0 "on" the surface, and positive "outside" the surface.
		Subclasses of Implicit need to define the function defining the implicit surface: double proc(gmVector3 x) and should define an interval proc(Box b) as well.
	graphics.cs.uiuc.edu /surface/doc/classImplicit.html (1688 words)

	Nilo Stolte Home page - Implicit Surfaces
		These images were obtained by transforming implicit surfaces to voxels (a process called voxelization) using interval arithmetic and then rendered by displaying each voxel as a 3D point with a normal vector using OpenGL Z-buffer.
		Implicit Surfaces can be blended together using a blending function.
		The blended spheres surface shown in the previous image was voxelized in 14 seconds using 1 master and seven slaves, each running in a different R10000 processor in a SGI Challenge.
	nilo.stolte.free.fr /graphics.html (708 words)

	Implicit surface - Wikipedia, the free encyclopedia
		In mathematics and computer graphics, an implicit surface is defined as an isosurface—a level set—of a function
		To find a parametrisation of the 'surface' (more precisely the solution set, since not all equations of this type define a surface, or indeed define any points at all) one has to treat this relation as giving an implicit function
		When the function f is a polynomial in the three variables then the surface is an algebraic surface (over the reals).
	en.wikipedia.org /wiki/Implicit_surface (163 words)

	Interpolating and Approximating Implicit Surfaces from Polygon Soup
		The user can choose to generate a surface that exactly interpolates the polygons, or a surface that approximates the input by smoothing away features smaller than some user-specified size.
		The implicit functions are represented using a moving least-squares formulation with constraints integrated over the polygons.
		The paper also presents an improved method for enforcing normal constraints and an iterative procedure for ensuring that the implicit surface tightly encloses the input vertices.
	www.cs.berkeley.edu /b-cam/Papers/Shen-2004-IAI (481 words)

	Assignment 2: Visualization Techniques for Stream Surfaces - A Report
		Implicit Stream Surfaces: Implicit Stream Surface is based on the representation of a stream surface as an implicit surface f(x) = C [2].
		The dataset containing the Scalar values (of the implicit) function are passed to a contour filter which does a Marching Cubes or a similar algorithm to extract an iso surface.
		This iso surface corresponds to a stream surface generated by an implicit curve on the inflow boundary chosen.
	www.mech.utah.edu /~amba/cs7961/Assign2 (2111 words)

	Implicit Surface Algorithm
		Given a point of an implicitly defined surface with full rank Jacobian, the implicit function theorem guarantees that there is some neighborhood in the tangent space that maps into the surface in a bijective manner.
		Starting with a point on the surface, Henderson's algorithm computes the exponential map in a small elliptic region in the tangent space using many applications of Newton's method.
		This is an example of a 2-dimensional surface in 4-dimensional space.
	www.geom.uiuc.edu /docs/forum/henderson (783 words)

	CRUISE:Cortical Reconstruction Using Implicit Surface Evolution (Site not responding. Last check: 2007-11-06)
		The cortical GM is bounded by the cerebrospinal fluid (CSF) on the outside, forming the pial cortical surface, and by the white matter (WM) on the inside, forming the inner cortical surface.
		It is useful to define the central cortical surface as well, which lies at roughly the geometric center between the inner and pial surfaces and gives an overall 2-D approximation to the 3-D cortical sheet.
		An additional nesting constraint is imposed during the implementation to ensure that the extracted surfaces are properly nested (the central inside the pial, and the inner inside the central).
	iacl.ece.jhu.edu /projects/cruise (1312 words)

	3D VSSP: Geometric Fusion
		An implicit surface based approach has been developed for integration of multiple triangulated meshes into a single representation.
		The implicit surface based geometric fusion approach has been applied to modelling both isolated objects and internal enviroments.
		Implicit surface polygonisation is achieved using the Marching Triangles approach.
	www.ee.surrey.ac.uk /Research/VSSP/3DVision/geomfuse.html (498 words)

	Advanced Surface Library: Implicit.h File Reference
		Macro to construct a new subclass of Implicit.
		This is pretty much just a Implicit* but the auto_ptr adds some safety mechanisms to avoid memory leaks.
		Hate to put this here of all places, but want to keep libgm unchanged and this is the only file I know will be included by everyone.
	graphics.cs.uiuc.edu /surface/doc/Implicit_8h.html (400 words)

	Tetrahedra Based Adaptive Polygonization of Implicit Surface Patches (Abstract) (Site not responding. Last check: 2007-11-06)
		An implicit surface patch is defined as an implicit surface bounded by its intersections with a set of clipping surfaces and which lies within an enclosing tetrahedron.
		To obtain the polygonization of an implicit surface patch, the tetrahedron containing the patch is adaptively subdivided into smaller tetrahedra according to the criteria introduced in the paper.
		The intersections between the facets and the clipping surfaces are used to locate the surface patch boundary.
	www.eg.org /EG/CGF/Volume18/Issue1/cgf302.html (195 words)

	ARANZ: Implicit Surface Representations (Site not responding. Last check: 2007-11-06)
		Representing objects and their surfaces implicitly with a mathematical function has a number of advantages.
		There are generally fewer terms in the function than vertices in the raw surface data.
		New RBF fitting techniques and RBF filters allow smooth surfaces to be reconstructed from very noisy data.
	aranz.com /research/modelling/theory/surfacerep.html (231 words)

	CS418 Lab 11
		Implicit surfaces are generated by finding "level surfaces" in a 3D field.
		when a surface is fit to the points in 3D which have a value of zero.
		(Remember that an implicit function changes sign as the surface is crossed and that for the surfaces used here, that points inside have a negative value.) The image below is the result of the union of two cylinders.
	instruct1.cit.cornell.edu /courses/cs418-land/lab11.html (836 words)

	Farfield: Surface modelling - FAQ (Site not responding. Last check: 2007-11-06)
		The object's surface is defined implicitly as the zero set of this function.
		The surface is implicitly defined as the zero-valued iso-surface of this function.
		An iso-surfacing routine is used to generate an explicit mesh representations from the implicit representation.
	www.farfieldtechnology.com /products/toolbox/theory/surfacefaq.html (513 words)

	Adaptive Implicit Surface Polygonization Using Marching Triangles (Abstract) (Site not responding. Last check: 2007-11-06)
		This paper presents several improvements to the marching triangles algorithm for general implicit surfaces.
		We present several modifications to adapt the size of the triangles to the curvature of the surface.
		In contrast to existing incremental techniques based on spatial subdvision, no extra data-structure is needed to incrementally edit skeletal implicit surfaces, which saves both memory and computation time.
	www.eg.org /EG/CGF/volume20/issue2/cgf479.html (156 words)

	Portfolio
		A physics demonstration of a ball bouncing on a implicit surface.
		The surface consisted of 5000 polygons and the ray test was doing a linear search through them.
		I think it would actually make more sense to ray test the moving sphere against the surface, that would allow me to only do one ray cast, but it would probably be a more computationally expensive one.
	www.mindspring.com /~paster/gravity.html (661 words)

	Algebraic Level Solver
		By default the surface will be coloured according to the x,y,z values of individual points.
		By default the surface will be drawn with faces (elements) visible, edges, lines and vertices not visible.
		If you want to calculate more complicated surfaces please send an email to Richard Morris at pfaf@webmaster.org or look at his website and he'll provide a version you can run at home which does not have the timeout restriction.
	www.javaview.de /services/algebraic/index.html (805 words)

	CImplicitSurfaceViewerDoc class Reference
		Extract surface points from the vertices of an alpha-complex shape, using the centre of gravity also if lGravity is true.
		Minimum number of points in an implicit surface for it not to be eliminated.
		Batch generates the vertices, triangles and normals for a given implicit surface.
	vrlab.epfl.ch /~lorna/doxygen/ImplicitSurfaceViewer/classCImplicitSurfaceViewerDoc.html (1734 words)

	Implicit-Surface Ray-Tracer
		The program should be able to read a text file and extract the definition of the scene consisting of light, root extraction iteration and gaussian implicit function parameters.
		The root finding algorithm returns the root of a sum of implicit gaussian functions specified in a text file and represents the position light rays intercept the implicit surface.
		This is done by calculating the normal to the surface at each root computed.
	www.geocities.com /bsgama/index.html (1151 words)

	Surface library with Particle System (Site not responding. Last check: 2007-11-06)
		The Surface Constrained Particle System library is designed to support research and development of new shape modeling tools.
		Its main components include a broad library of implicit surface representations, and a sophisticated particle system structure for interrogating implicit surfaces.
		Here is a link to the surface modeling class that was offered in Fall 2000.
	graphics.cs.uiuc.edu /projects/surface (237 words)

	Surface Modeling
		POVRAY isosurface renders an equipotential surface defined by an implicit equation and bound constraints
		Surface Reconstruction from Unorganized Points (html, Ph.D. Thesis by Hugues Hoppe)
		Curves and Surfaces Saint-Malo (France), July 1-7, 1999.
	www.mat.univie.ac.at /~neum/surface.html (290 words)

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