https://f-rep.org/ 2026-04-24T22:29:11+00:00 https://f-rep.org/ https://f-rep.org/_media/wiki/dokuwiki.svg text/html 2023-12-19T03:07:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/appletinfo?rev=1702955254&do=diff HyperFun: Applet info Default parameters: Bounding box: (-5, -5, -5), (5, 5, 5) Grid resolution: (x, y, z) = (30, 30, 30) Supported FRep library primitives and operations Primitives: * hfSphere * hfEllipsoid * hfCylinderX * hfCylinderY * hfCylinderZ text/html 2023-12-19T03:07:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/contact?rev=1702955254&do=diff Contact HyperFun language, software tools, and applications are being developed by the team members worldwide. If you have questions or comments, you may contact each of them personally or send e-mail to reach the entire development team. To subscribe to the HyperFun mailing list click text/html 2023-12-19T03:07:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/events?rev=1702955254&do=diff HyperFun: News and Events * FRep and HyperFun in the course How To Make Something That Makes (almost) Anything at MIT, 2012 * HyperFun in the Advanced Graphics course at the University of Cambridge, UK, 2011-2012 * Another free FRep modelling system: Symvol for Rhino - Maker version developed by Uformia, Norway, in partnership with the Digital Materialization Group, Japan-UK, October 2011. text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fab_chess?rev=1702955252&do=diff HyperFun Fabrication: Chess Equipment: SLA 3500 stereolithography system by 3D Systems. Material: resin text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fab_fablab?rev=1702955252&do=diff HyperFun in the Fab Lab Fab Lab User Group Meeting. Programming and Modeling Workshop MIT-FabLab Norway, Lyngen, August 10-17, 2005 The main goal of the workshop is to present the step-by-step practical use of the HyperFun language and tools for shape modeling and fabrication in the Fab Lab environment. text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fab_hon?rev=1702955252&do=diff HyperFun Fabrication: Kanji Hon Relief carving of the Japanese character Hon (book). HyperFun model: Hon_relief.hf (1.8 Kb) Equipment: Modela MDX-20 milling machine by Roland DG. Material: wood text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fab_jewelry?rev=1702955252&do=diff <code class="code html4strict"><span class="sc2">&lt;<a href="http://december.com/html/4/element/b.html"><span class="kw2">b</span></a>&gt;&lt;<a href="http://december.com/html/4/element/span.html"><span class="kw2">span</span></a> <span class="kw3">style</span><span class="sy0">=</span><span class="st0">&quot;font-size:20px;&quot;</span>&gt;</span>Fabricating Custom Jewelry Designs Using Math!<span class="sc2">&lt;<span class="sy0">/</span><a href="http://december.com/html/4/element/span.html">… text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fab_turtle?rev=1702955252&do=diff HyperFun Fabrication: Turtle Equipment: Modela MDX-20 milling machine by Roland DG. Material: wood text/html 2023-12-19T03:07:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fablab_ant?rev=1702955253&do=diff HyperFun in the Fab Lab: Ant * Ant model from the HyperFun Gallery (with removed feelers) * Equipment: Modela MDX-20 milling machine by Roland DG. * Material: modeling wax * Size of the fabricated model: 10 mm Wax ant top Zoom text/html 2023-12-19T03:07:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fablab_carving?rev=1702955253&do=diff HyperFun in the Fab Lab: Relief carving We use the HyperFun Polygon Convertor: a 2D polygon drawing tool (polygon.exe) and a convertor from a polygon to HyperFun (Polygon_FRep.exe) for modeling a relief for carving. Then, we carve the generated relief on a block and on a spoon. text/html 2023-12-19T03:07:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fablab_clip?rev=1702955253&do=diff HyperFun in the Fab Lab: Sheep ear clip * Design specification by Jorgen Karlsen (MIT-FabLab Norway) * The HyperFun model: sheepclip.hf * The bounding box is x,y: [-0.5,5] z:[-0.5, 2.5] * Equipment: Modela MDX-20 milling machine by Roland DG. * Material: modeling wax Prototype clip text/html 2023-12-19T03:07:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fablab_doggy?rev=1702955253&do=diff HyperFun in the Fab Lab: Mutant doggy * Design specification by Grace Gershenfeld (8 years old) and Michael Angst (The Fab Company) * The HyperFun model: doggy.hf * The bounding box is [-5,5] * Material: Modelling Foam Mutant Doggy model Modela Player (STL) text/html 2023-12-19T03:07:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fablab_horse?rev=1702955253&do=diff HyperFun in the Fab Lab: Norwegian horse * Design specification by Haakon Karlsen (MIT-FabLab Norway) * Painting of the fabricated model by Hanne-Christine Skogheim * The HyperFun model: horse.hf * The bounding box is x:[0,20], y:[0,8], z:[0,20] * text/html 2023-12-19T03:07:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fablab_mold?rev=1702955253&do=diff HyperFun in the Fab Lab: Plastic mold * Design specification by Balu Badu Jadhav and Yogesh Ramesh Kulkarni (Vigyan Ashram FabLab, India) * The HyperFun model: mold.hf * The bounding box for HFP -b -0.5,-0.5,-0.5,8.5,8.5,3.5 text/html 2023-12-19T03:07:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fablab_spoon?rev=1702955253&do=diff HyperFun in the Fab Lab: Making a Japanese spoon 1. HyperFun model: jspoon.hf 2. Render the model with the bounding box x:[0,17], y:[0,5], z:[0.3] 3. Generate an STL file with the grid 100 or higher 4. Fabricate the model using Modela MDX milling machine. text/html 2023-12-19T03:07:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fablab_torus?rev=1702955253&do=diff HyperFun in the Fab Lab: Making a simple cut torus 1. Type or copy the HyperFun model: toruscut.hf 2. Render the model with the bounding box x:[0,6], y:[0,6], z:[0,1.2] 3. Generate an STL file with the grid 100 or higher 4. Fabricate the model using Modela MDX milling machine (see two photos of a wooden cut torus above). text/html 2023-12-19T03:07:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/fabrication?rev=1702955253&do=diff HyperFun: Fabrication Jewelry Augmented Sculpture Chess Kanji Hon FabLab Norway models Turtle text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hf_applet?rev=1702955252&do=diff HyperFun: Applet <http://hyperfun.org/hfapplet/hfapplet.html> Usage To run the applet * Check if the required Java tools are installed. * Click on the image above to load the applet. * Click the “Polygonize” button to test. * Rotate the object using left mouse button. Requirements text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hf_comments?rev=1702955251&do=diff HyperFun: Comments, Names, Case Sensitivity Throughout the description, all reserved (“key”) words and literals will be surrounded by apostrophes `...'. Comments Any text beginning from '--' to the end of the current line will be ignored by the parser. Example: text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hf_dor?rev=1702955251&do=diff HyperFun: Cat model my_model(x[3], a[1]) { array head1Cent[3], hana1Cent[3], xface1Cent[3], xface2Cent[3], xkuti1Cent[3], eye1Cent[3], eye2Cent[3], eye4Cent[3], eye6Cent[3], eye8Cent[3], body1Cent[3], cubiwaCent[3], suzuCent[3], hara1Cent[3], hara2Cent[3], hara4Cent[3], hara5Cent[3], xllegCent[3], xrlegCent[3], xlfootCent[3], xrfootCent[3], rhige1Cent[3], rhige2Cent[3], rhige3Cent[3], xlhige1Cent[3], xlhige2Cent[3], xlhige3Cent[3], hand1Cent[3], hand2Cent[3], ude1Cent[3]; xx=x[1]; y=x[2]; … text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hf_objects?rev=1702955251&do=diff HyperFun: Objects A geometric object is supposed to have semantically significant geometric sense. The general form of the object's structure is: <objectName> '(' 'x' '[' <size> ']' ',' 'a' '[' <size> ']' ',' 's' '[' <size> ']'')' '{' [<array declarations>] text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hf_operators?rev=1702955251&do=diff HyperFun: Operators and Expressions There are two types of expressions permissible in the language: 'functional' expression and 'logical' expression. Functional expression The functional expression is a conventional numerical expression built with using: text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hf_program?rev=1702955251&do=diff HyperFun: Program The program in HyperFun consists of one or few objects defined one after another. The previous objects can be used in functional expressions of the following ones. Example of a program without attributes: -- The program contains the definitions of three objects -- Definition of object "Parallelepiped" Parallelepiped(x[3], a[6]) { Parallelepiped = (x[1] - a[1]) & (-(x[1] - a[1]) + a[4]) & (x[2] - a[2]) & (-(x[2] - a[2]) + a[5] & (x[3] - a[3]) & (-(x[3] - a[3]) + a[6])); } -… text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hf_sample?rev=1702955251&do=diff HyperFun: sample model Sample model without attributes --This HyperFun program consists of one object: --union of superellipsoid, torus and soft object my_model(x[3], a[1]) { array x0[9], y0[9], z0[9], d[9], center[3]; x1=x[1]; x2=x[2]; x3=x[3]; -- superellipsoid by formula superEll = 1-(x1/0.8)^4-(x2/10)^4-(x3/0.8)^4; -- torus by library function center = [0, -9, 0]; torus = hfTorusY(x,center,3.5,1); -- soft object x0 = [2.,1.4, -1.4, -3, -3, 0, 2.5, 5., 6.5]; y0 = [8, 8, 8, 6.5, 5, 4.… text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hf_statements?rev=1702955251&do=diff HyperFun: Statements There are four types of the statements each ending with ';': * Assignment statement for a variable * Assignment statement for an array * Conditional statement * Iterative statement Assignment statement for a variable. Its general form is: <localVarName> '=' <functional expression> ';' Here <localVarName> is a name of any local variable (including name of array's element) or a name of a coordinate variable. Examples: text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hf_types?rev=1702955251&do=diff HyperFun: Types, Variables and Declarations There are two fundamental types for variables ('real' and 'array') and an additional one ('string'). Real 'Real' is the only elementary numeric type that is floating-point type and is equivalent to a 'double' type in C. Note that one can use integer constants but they are treated as a subclass of the same floating-point type; there is no explicit Boolean type but in the relational operators the floating-point value '0.' is treated as 'false', and ot… text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hfp_documentation?rev=1702955252&do=diff HyperFun Polygonizer This executable polygonizes and displays an object from a HyperFun file. With this version you can also export a VRML version of the output. All options are set at the command line as is described in the Usage section below. The options can be changed using the keys as shown at the bottom of the window. text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hfpolygon_readme?rev=1702955252&do=diff HyperFun Polygon Convertor This is a Windows tool for 2D polygon drawing and conversion to HyperFun. There are two programs: 1) polygon.exe is a simple Windows editor for a 2D polygon: * press left mouse button - add vertex * double click - close the polygon text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hfpov_readme?rev=1702955252&do=diff POV-Ray 3.6 with HyperFun support This is unofficial build of POV-ray ray-tracer. A new keyword was added to support HyperFun models. Installation First, you need to download and install official POV-Ray 3.6 from here. After that, you need to download POV-Ray binaries with HyperFun support from text/html 2023-12-19T03:07:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hfw_gallery?rev=1702955252&do=diff HyperFun for Windows: Graphics and Animation Static images The images below (except the isosurface) are generated using the following model: fsin(x[2], a[1]){ d=x[1]^2+x[2]^2; fsin = sin(d)*exp(-sqrt(d)); } The table below shows the available image types and corresponding assignement of coordinates X Assign and function F Assign. Click on an image below to get its larger size version. text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/hyperfox_manual?rev=1702955251&do=diff Hyperfox Supported commands These commands can be used from javascript for configuring the visualization window: * void setSource(string) : Sets the source for the model. The input string is the program on HyperFun langugage. * boolean isFloat(string) : Checks if the input string is floating-point variable. text/html 2023-12-19T03:07:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/introduction?rev=1702955251&do=diff Introduction HyperFun Project is a free software development project for functionally based shape and volume modeling, visualization, animation, and fabrication. The project is based on the Function Representation (FRep) of geometric objects and supporting software tools built around the text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/language?rev=1702955250&do=diff HyperFun: Language for FRep Volume Modeling HyperFun is intended for describing both object's geometry in the form <m>F(x_1, x_2, x_3, ..., x_n) >= 0</m> and object's attributes at any point of n-dimensional space in the form <m>S_i = S_i(x_1, x_2, x_3, text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_attrnoise?rev=1702955250&do=diff Noise and turbulence functions for texture patterns Primitive: Gardner Solid Noise Definition: Series(x)*Series(y)*Series(z) with Gardner's series Call: hfA_NoiseG(x,freq,phase); Parameters: x - point coordinates array freq - noise frequency text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_attrset?rev=1702955250&do=diff Applying a set of attributes and union operation Set Attributes Definition: if(fв%_0) then s=c Call: hfA_SetAttributes(f,s,c); Parameters: f - real values s - Output Array c - array of attributes Output : array s Test file: hfA_SetAttributes.hf Set Colors text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_attrtoolbox?rev=1702955250&do=diff Toolbox functions Clamp Definition: min(max(f,a),b) Call: hfA_Clamp(f,a,b); Parameters: f : real value (to be clamped) a : lower boundary of the interval b : upper boundary of the interval Step Definition: if f<a return 0 else return 1 Call text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_atttex?rev=1702955250&do=diff Texture patterns and look up table Pattern: Waves Definition: t = (1+sin(freq*xt))/2.0 attribute = a0+t*(a1-a0) Call: hfA_Wave(xt,a0,a1,freq); Parameters: xt - point coordinate a0,a1 - Interval in between the returned value belongs freq - Frequency text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_bezier?rev=1702955250&do=diff Primitive: Bézier spline object [Schmitt, Pasko, and Savchenko 1999] Definition: Object defined by F>=0, where F is a Bezier spline function of three variables <m>F(u,v,w) = sum{i=0}{l}{}sum{j=0}{n}{}sum{k=0}{m}{}B_i(u)B_j(v)B_k(w)P_{ijk}</m> <m>P_{ijk}</m> - Control points of the Bézier volume. Only the fourth coordinnate is used text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_blendint?rev=1702955250&do=diff Transformation: Blending Intersection [Pasko and Savchenko 1994] Definition: <m>R_{int}(f1,f2) + disp(f1,f2,a0,a1,a2)</m> <m>disp(f1,f2,a0,a1,a2)=a0/{1+(f1/a1)^2+(f2/a2)^2}</m> Call: hfBlendInt(f1,f2,a0,a1,a2); Parameters: f1,f2 - two objects a0,a1,a2 - blend parameters text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_blenduni?rev=1702955250&do=diff Transformation: Blending Union [Pasko and Savchenko 1994] Definition: <m>R_uni(f1,f2) + disp(f1,f2,a0,a1,a2)</m> <m>disp(f1,f2,a0,a1,a2)=a0/{1+(f1/a1)^2+(f2/a2)^2}</m> Call: hfBlendUni(f1,f2,a0,a1,a2); Parameters: f1,f2 - two objects a0,a1,a2 - blend parameters text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_blobby?rev=1702955250&do=diff Primitive: Blobby object [Blinn 1982] Definition: <m>sum{}{}{b*e^{-a*r^2}-T}</m> Call: hfBlobby(x,x0,y0,z0,a,b,T); Parameters: x - point coordinates x0,y0,z0 - arrays of blob centers a - array of a coefficients b - array of b coefficients T - threshold value text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_block?rev=1702955249&do=diff Primitive: Block Definition: x:[vertex[1], vertex[1]+dx], ... Call: hfBlock(x,vertex,dx,dy,dz); Parameters: x - point coordinates array vertex - block vertex coordinates array dx,dy,dz - edge lengths along x,y,z Test file: block.hf text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_cone?rev=1702955249&do=diff Primitive: Cone with x-axis Definition: <m>(x-x_0)^2-(y-y_0)^2/R^2-(z-z_0)^2/R^2</m> Call: hfConeX(x,center,R); Parameters: x - point coordinates array center - cone apex array R - cone radius at height=1 Test file: cone.hf Primitive: Cone with y-axis text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_convarcs?rev=1702955249&do=diff Primitive: Convolution with set of skeleton arcs Definition: <m>sum{}{}{f(r)}</m> f(x) is analytical convolution for an arc with Cauchy kernel [McCormack and Sherstyuk 1998] r - distance to a skeleton point Call: hfConvArc(x,center,radius,theta,axis,angle,S,T); text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_convcurve?rev=1702955249&do=diff Primitive: Convolution with curve (set of connected skeleton line segments) Definition: <m>sum{}{}{f(r)}</m> f(x) is analytical convolution for a segment with Cauchy kernel [McCormack and Sherstyuk 1998] Call: hfConvCurve(x,vect,S,T); Parameters text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_convline?rev=1702955249&do=diff Primitive: Convolution with set of skeleton line segments Definition: <m>sum{}{}{f(r)}</m> f(x) is analytical convolution for a segment with Cauchy kernel [McCormack and Sherstyuk 1998] r - distance to a skeleton point Call: hfConvLine(x,begin,end,S,T); text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_convmesh?rev=1702955249&do=diff Primitive: Convolution with mesh (set of connected triangles) Definition: <m>sum{}{}{f(r)}</m> f(x) is analytical convolution for a triangle with Cauchy kernel [McCormack and Sherstyuk 1998] Call: hfConvMesh(x,vect,tri,S,T); Parameters: x - point coordinates text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_convpoint?rev=1702955249&do=diff Primitive: Convolution with set of skeleton points Definition: <m>sum{}{}{f(r)}</m> <m>f(r)= 1/(1 + S^2*r^2)^2</m>, Cauchy kernel [McCormack and Sherstyuk 1998] r - distance to a skeleton point Call: hfConvPoint(x,vect,S,T); Parameters: x - point coordinates text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_convtri?rev=1702955249&do=diff Primitive: Convolution with set of triangles Definition: <m>sum{}{}{f(r)}</m> f(x) is analytical convolution for a triangle with Cauchy kernel [McCormack and Sherstyuk 1998] r - distance to a skeleton point Call: hfConvTriangle(x,vect,S,T); Parameters text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_cubicspace?rev=1702955249&do=diff Transformation: Cubic space mapping Definition: Space mapping (deformation) controlled by moving arbitrary points in space. Inverse Mapping: <m>x{prime} = x - sum{}{}{{delta x_i}*(1-v_i)^3/(1+v_i)}</m> <m>y{prime} = y - sum{}{}{{delta y_i}*(1-v_i)^3/(1+v_i)}</m> text/html 2023-12-19T03:07:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_cubicspline?rev=1702955249&do=diff Primitive: Cubic B-spline object [Schmitt et al. 2000] Definition: Object defined by F>=0, where F is a B-spline function of three variables <m>F(u,v,w) = sum{i=0}{l}{}sum{j=0}{n}{}sum{k=0}{m}{}N_i(u)N_j(v)N_k(w)P_{ijk}</m> <m>P_{ijk}</m> - Control points of the cubic B-spline volume. Only the fourth coordinnate is used text/html 2023-12-19T03:07:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_cylinder?rev=1702955248&do=diff Primitive: Cylinder with x-axis Definition: <m>R^2-(y-y_0)^2-(z-z_0)^2</m> Call: hfCylinderX(x,center,R); Parameters: x - point coordinates array center - cylinder center array R - cylinder radius Test file: cylinder.hf Primitive: Cylinder with y-axis text/html 2023-12-19T03:07:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_dcone?rev=1702955248&do=diff Primitive: Cone with distance property (x-axis) Call: hfDConeX(x,center,R); Parameters: x - point coordinates array center - cone apex array R - cone radius at height=1 Primitive: Cone with distance property (y-axis) Call: hfDConeY(x,center,R); text/html 2023-12-19T03:07:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_dcylinder?rev=1702955248&do=diff Primitive: Cylinder with distance property Call: hfDCylinder(x, center, d, R); Parameters: x - point coordinates array center - cylinder center array d - cylinder axis direction array R - cylinder radius text/html 2023-12-19T03:07:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_dellipsoid?rev=1702955248&do=diff Primitive: Ellipsoid with distance property Call: hfDEllipsoid(x,center,a,b,c); Parameters: x - point coordinates array center - ellipsoid center array a, b, c - ellipsoid half-axes along x, y, z text/html 2023-12-19T03:07:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_dops?rev=1702955248&do=diff SARDF operations [Fayolle et al 2006] Transformation: SARDF Union Call: hfDUni(f1,f2); Parameters: f1,f2 - two objects Transformation: SARDF Intersection Call: hfDInt(f1,f2); Parameters: f1,f2 - two objects Transformation: SARDF Subtraction text/html 2023-12-19T03:07:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_dtorus?rev=1702955248&do=diff Primitive: Torus with distance property (x-axis) Call: hfDTorusX(x,center,R,r0); Parameters: x - point coordinates array center - cylinder center array R - radius of revolution r0 - disk radius Primitive: Torus with distance property (y-axis) text/html 2023-12-19T03:07:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_ellcone?rev=1702955248&do=diff Primitive: Elliptic cone with x-axis Definition: <m>(x-x_0)^2-(y-y_0)^2/a^2-(z-z_0)^2/b^2</m> Call: hfEllConeX(x,center,a,b); Parameters: x - point coordinates array center - cone apex array a,b - elliptic half-axes along y, z at the distance 1 along x text/html 2023-12-19T03:07:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_ellcyl?rev=1702955248&do=diff Primitive: Elliptic cylinder with x-axis Definition: <m>1-(y-y_0)^2/a^2-(z-z_0)^2/b^2</m> Call: hfEllCylX(x,center,a,b); Parameters: x - point coordinates array center - cylinder center array a,b - elliptic half-axes along y,z Test file: ellcyl.hf Primitive: Elliptic cylinder with y-axis text/html 2023-12-19T03:07:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_ellipsoid?rev=1702955248&do=diff Primitive: Ellipsoid Definition: <m>1-((x-x_0)/a)^2-((y-y_0)/b)^2-((z-z_0)/c)^2</m> Call: hfEllipsoid(x,center,a,b,c); Parameters: x - point coordinates array center - ellipsoid center array a,b,c - ellipsoid half-axes along x,y,z Test file: ellipsoid.hf text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_metaball?rev=1702955247&do=diff Primitive: Metaballs object [Nishimura et al. 1985] Definition: <m>Sum{}{}{f(r)}-T</m>, <m>f(r)=delim{lbrace}{matrix{3}{1}}{ }</m> r - distance to the given point Call: hfMetaball(x,x0,y0,z0,b,d,T); Parameters: x - point coordinates x0,y0,z0 - arrays of mataball centers text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_noise?rev=1702955247&do=diff Primitive: Solid noise Definition: Series(x)*Series(y)*Series(z) with Gardner's series [Gardner 1984] Call: hfNoiseG(x,amp,freq,phase); Parameters: x - point coordinates array amp - noise amplitude freq - noise frequency phase - phase for sin() in the series text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_rotate?rev=1702955247&do=diff Transformation: Rotation in 3D around z-axis Definition: inverse mapping x'=x*cos(theta)+y*sin(theta) y'=-x*sin(theta)+y*cos(theta) Call: hfRotate3DZ(xt,theta); Parameters: xt - point coordinates array to be changed theta - rotation angle in radians text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_scale?rev=1702955247&do=diff Transformation: Scale in 3D space Definition: x'=sx*x Call: hfScale3D(xt,sx,sy,sz); Parameters: xt - point coordinates array to be changed sx,sy,sz - scaling factors along axes Test file: scale.hf text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_shift?rev=1702955247&do=diff Transformation: Shift in 3D space Definition: x'=x+dx Call: hfShift3D(xt,dx,dy,dz); Parameters: xt - point coordinates array to be changed dx,dy,dz - scaling factors along axes Test file: shift.hf text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_soft?rev=1702955247&do=diff Primitive: Soft object [Wyvill et al. 1986] Definition: <m>f(r)= 1 - 22*r^2/{9*d^2} + 17*r^4/{9*d^4} - 4*r^6/{9*d^6}</m> r - distance to the given point Call: hfSoft(x,x0,y0,z0,d,T); Parameters: x - point coordinates x0,y0,z0 - arrays of blob centers text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_sphere?rev=1702955247&do=diff Primitive: Sphere (ball) Definition: <m>R^2-(x-x_0)^2-(y-y_0)^2-(z-z_0)^2</m> Call: hfSphere(x,center,R); Parameters: x - point coordinates array center - sphere center array R - sphere radius Test file: sphere.hf text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_stretch?rev=1702955247&do=diff Transformation: Stretching in 3D space Definition: x'=x0+(x-x0)/scale (inverse mapping) Call: hfSTretch3D(xt,x0,sx,sy,sz); Parameters: xt - point coordinates array to be changed x0 - reference point for stretching sx,sy,sz - scaling factors along axes text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_superell?rev=1702955247&do=diff Primitive: Superellipsoid Definition: <m>1-(((x-x_0)/a)^2/s2+((y-y_0)/b)^2/s2)^(s2/s1)-((z-z_0)/c)^(2/s1)</m> Call: hfSuperell(x,center,a,b,c,s1,s2); Parameters: x - point coordinates array center - center array a,b,c - half-axes along x,y,z s1, s2 - shape parameters, s1 - text/html 2023-12-19T03:07:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_taper?rev=1702955247&do=diff Transformation: Tapering along z-axis Definition: inverse mapping z1<= z <= z2 t = (z-z1)/(z2-z1) scale = (1-t)*s1 + t*s2 x'=x/scale y'=y/scale z < z1 scale = s1 z > z2 scale = s2 Call: hfTaperZ(xt,z1,z2,s1,s2); Parameters: xt - point coordinates array to be changed text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_torus?rev=1702955246&do=diff Primitive: Torus with X-axis Definition: <m>{r_0}^2-(x-x_0)^2-(y-y_0)^2-(z-z_0)^2-R^2+2*R*sqrt{(z-z_0)^2+(y-y_0)^2}</m> Call: hfTorusX(x,center,R,r0); Parameters: x - point coordinates array center - center array R - radius of revolution r0 - disk radius text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/lib_twist?rev=1702955246&do=diff Transformation: Twisting around z-axis Definition: inverse mapping t = (z-z1)/(z2-z1) theta = (1-t)*theta1 + t*theta2 x'=x*cos(theta)+y*sin(theta) y'=-x*sin(theta)+y*cos(theta) Call: hfTwistZ(xt,z1,z2,theta1,theta2); Parameters: xt - point coordinates array to be changed text/html 2023-12-19T03:07:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/library?rev=1702955250&do=diff HyperFun: FRep Library Primitives * Sphere * Ellipsoid * Cylinder * Elliptic cylinder * Cone * Elliptic cone * Torus * Superellipsoid * Block * Blobby object * Metaballs * Soft object * Convolution object with skeleton: * Points * Line segments * Arcs * Triangles * Curve * Mesh * Solid noise * Objects based on parametric functions: * Cubic B-spline object * Bezier spline object * Primitives with distance properties text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/main?rev=1702955246&do=diff Welcome to HyperFun HyperFun is a simple specialized high-level programming language. It is intended for modeling geometric objects and their internal volumetric properties (color, material density and others). A model can include objects of mixed dimensions (1D, 2D, 3D, 4D and even kD)) defined by real functions of point coordinates. This language is applicable to modeling using algebraic, skeleton-based, and procedural text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/new?rev=1702955246&do=diff HyperFun: What's new? 10.10.2011 Another free FRep modelling system: Symvol for Rhino - Maker version developed by Uformia, Norway, in partnership with the Digital Materialization Group, Japan-UK 27.12.2008 Release of the HyperFun 2.0 language specification and software tools supporting volumetric modeling including both object geometry and attributes. text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/old_povray?rev=1702955246&do=diff Isosurface Patch for POV-Ray 3.1 ver:1.11 11/23/2000 This is the Isosurface Patch for POV-Ray that allows you to raytrace HyperFun models on the Windows 9X and NT 4.0 platforms. Please read the readme file for more information and installation instructions. text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/related?rev=1702955246&do=diff HyperFun: Related projects * Constructive Texturing Plug-in to PointShop3D by C. Schlick and P. Reuter * Function-based Node of Virtual Reality Modelling Language by A. Sourin * HyperFun project and VRML language by J. Zara * |Implicit Surface Polygonizer by V. Skala and M. Cermak * Interactive System for Generating and Modeling Implicit Functions by V. Skala and K. Uhlir text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/sidebar?rev=1702955246&do=diff Main menu HyperFun Introduction HyperFun spec, ver. 2.0 Overview ( PDF ) Tutorial Tools Applications Gallery Fabrication News and Events Related projects Team Sponsors Contact & Mailing List What's new? FRep FRep main page What is FRep? Selected topics Gallery Publications Relative sites What's new? text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/sponsors?rev=1702955246&do=diff HyperFun Project Sponsors Alphabetic order CITEC, University of Aizu, Japan * Ikegami, T. Compufarm, Japan * Fausett E. and Sundberg C. Computer Arts Lab., University of Aizu, Japan * Vilbrandt C. and J. Eyes, Japan * Yamadera J. Faculty of Computer and Information Sciences, Hosei University , Japan * Ohmori K. IT Institute, Kanazawa Institute of Technology, Japan * Kunii T. Shape Modeling Lab., University of Aizu, Japan text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/team?rev=1702955246&do=diff HyperFun: Team * Adzhiev V. (National Centre for Computer Animation, Bournemouth University, UK) * Cartwright R. (portability 4 media, UK) * Fausett E. (QNX Software Systems, Japan) * Fayolle P.-A. (University of Aizu, Japan) * Fryazinov O. (National Centre for Computer Animation, Bournemouth University, UK) text/html 2023-12-19T03:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tools?rev=1702955246&do=diff HyperFun Tools Tools with HF2.0 spec support HyperFun Polygonizer ver: 2.03 This is HyperFun Polygonizer (HFP) for MS Windows with the following changes: * attributes support * dual contouring added as a polygonization method * fixed polygons orientation in STL export<code class="code html4strict"><span class="sc2">&lt;<a href="http://december.com/html/4/element/a.html"><span class="kw2">a</span></a> <span class="kw3">href</span><span class="sy0">=</span><span class="st0">&quot;h… text/html 2023-12-19T03:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tut_about?rev=1702955245&do=diff About F-rep In F-rep (function representation), a geometric object is defined by a single real continuous function F(x1, x2, x3, ..., xn) >= 0. Let's think why F(x1, x2, x3, ..., xn) >= 0 can represent an object. A geometric object in 3D space is described by: the inside, the surface, and the outside. text/html 2023-12-19T03:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tut_eq?rev=1702955245&do=diff Let's try to model objects using equations In this example, we do a single division of infinite space. With this division, we create a solid object called halfspace. So, let's try to define the object using x[1], x[2], x[3]. Let's try the following halfspace program and polygonize with hfp. text/html 2023-12-19T03:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tut_intro?rev=1702955245&do=diff Introduction This tutorial describes how to model functionally defined geometric objects using HyperFun. Although HyperFun Polygonizer is referenced throughout the tutorial, any other available viewer of HyperFun models can be used for exercises. What is HyperFun? text/html 2023-12-19T03:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tut_poly?rev=1702955245&do=diff Brief reference of HyperFun Polygonizer In this reference, we use example1.hf created in Getting started, but you can use your own HyperFun file. Note that a HyperFun file name has to be placed just after the hfp command; i.e., if you polygonize foo.hf with some options, the command would take the form: text/html 2023-12-19T03:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tut_set?rev=1702955245&do=diff Set-theoretic operations Until now, we have used only one equation or the library function to model an object. But, it is not enough for complex objects. This page shows how to combine primitives to model more complex objects. Suppose A is a blue box, B is a yellow sphere. text/html 2023-12-19T03:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tut_sethf?rev=1702955245&do=diff Set-theoretic operations in HyperFun Now, we will use HyperFun to construct objects using set-theoretic operations, which were introduced in the previous section. If you do not understand the meaning of a term (union, intersection, subtraction), please refer to the previous pages. text/html 2023-12-19T03:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tut_start?rev=1702955245&do=diff Getting Started A Sphere We begin with a simple sphere. The program example1.hf describes a solid sphere: <m>5^2 - (x^2 + y^2 + z^2) >= 0</m> -- example1.hf my_model(x[3], a[1]) { my_model = 5^2 - (x[1]^2 + x[2]^2 + x[3]^2); } Did you save the program text/html 2023-12-19T03:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tut_trans?rev=1702955245&do=diff Let's try to shift, scale, rotate objects Let's try to shift objects Array x in my_model(x[3], a[1]) includes coordinates in three dimensions. The corresponding relationship is, x[1] -> x x[2] -> y x[3] -> z The following is an equation of a solid sphere which has its center as the origin and a radius of 5: <m>5^2 - (x^2 + y^2 + z^2) >= 0</m> The model in HyperFun: text/html 2023-12-19T03:07:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/hyperfun/tutorial_e?rev=1702955245&do=diff HyperFun Tutorial * Introduction * What is HyperFun? * How to get HyperFun tools? * About F-rep * Getting Started * A sphere * Use library function * Let's try to model objects using equations in HyperFun * Let's try to shift, scale, rotate objects * Let's try to shift objects * Let's try to scale objects * Let's try to rotate objects * Set-theoretic operations * Union A and B * Intersection A and B * Subtraction B from A, A from B * Combination o…