1<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 3//EN"> 2<HTML><HEAD> 3 <TITLE>User's Reference - SimplifySurface</TITLE> 4 <META HTTP-EQUIV="keywords" CONTENT="GRAPHICS VISUALIZATION VISUAL PROGRAM DATA 5MINING"> 6 <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1"> 7</HEAD><BODY BGCOLOR="#FFFFFF" link="#00004b" vlink="#4b004b"> 8 <TABLE width=510 border=0 cellpadding=0 cellspacing=0> 9 <TR> 10 <TD><IMG src="../images/spacer.gif" width=80 height=1></TD> 11 <TD><IMG src="../images/spacer.gif" width=49 height=1></TD> 12 <TD><IMG src="../images/spacer.gif" width=24 height=1></TD> 13 <TD><IMG src="../images/spacer.gif" width=100 height=1></TD> 14 <TD><IMG src="../images/spacer.gif" width=3 height=1></TD> 15 <TD><IMG src="../images/spacer.gif" width=127 height=1></TD> 16 <TD><IMG src="../images/spacer.gif" width=6 height=1></TD> 17 <TD><IMG src="../images/spacer.gif" width=50 height=1></TD> 18 <TD><IMG src="../images/spacer.gif" width=71 height=1></TD> 19 </TR> 20 <TR> 21 <TD colspan=9><IMG src="../images/flcgh_01.gif" width=510 height=24 alt="OpenDX - Documentation"></TD> 22 </TR> 23 <TR> 24 <TD colspan=2><A href="../allguide.htm"><IMG src="../images/flcgh_02.gif" width=129 height=25 border="0" alt="Full Contents"></A></TD> 25 <TD colspan=3><A href="../qikguide.htm"><IMG src="../images/flcgh_03.gif" width=127 height=25 border="0" alt="QuickStart Guide"></A></TD> 26 <TD><A href="../usrguide.htm"><IMG src="../images/flcgh_04.gif" width=127 height=25 border="0" alt="User's Guide"></A></TD> 27 <TD colspan=3><B><A href="../refguide.htm"><IMG src="../images/flcgh_05d.gif" width=127 height=25 border="0" alt="User's Reference"></A></B></TD> 28 </TR> 29 <TR> 30 <TD><A href="refgu141.htm"><IMG src="../images/flcgh_06.gif" width=80 height=17 border="0" alt="Previous Page"></A></TD> 31 <TD colspan=2><A href="refgu143.htm"><IMG src="../images/flcgh_07.gif" width=73 height=17 border="0" alt="Next Page"></A></TD> 32 <TD><A href="../refguide.htm"><IMG src="../images/flcgh_08.gif" width=100 height=17 border="0" alt="Table of Contents"></A></TD> 33 <TD colspan=3><A href="refgu009.htm"><IMG src="../images/flcgh_09.gif" width=136 height=17 border="0" alt="Partial Table of Contents"></A></TD> 34 <TD><A href="refgu175.htm"><IMG src="../images/flcgh_10.gif" width=50 height=17 border="0" alt="Index"></A></TD> 35 <TD><A href="../srchindx.htm"><IMG src="../images/flcgh_11.gif" width=71 height=17 border="0" alt="Search"></A></TD> 36 </TR> 37 </TABLE> 38 <H3><A name="HDRSIMPSUR" ></A>SimplifySurface</H3> 39 <P><STRONG>Category</STRONG> 40 <P> 41<A HREF="refgu008.htm#HDRCATTRN">Transformation</A> 42<P><STRONG>Function</STRONG> 43<P> 44Simplifies a triangulated surface and resamples data attached to the surface. 45<P><STRONG>Syntax</STRONG> 46<PRE> 47<STRONG>simplified</STRONG> = SimplifySurface(<STRONG>original_surface, max_error, max_data_error, 48 volume, boundary, length, data, stats</STRONG>); 49</PRE> 50<P><STRONG>Inputs</STRONG> 51<BR> 52<TABLE BORDER> 53<TR> 54<TH ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">Name 55</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">Type 56</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">Default 57</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">Description 58</TH></TR><TR> 59<TD ALIGN="LEFT" VALIGN="TOP" 60WIDTH="20%"><TT><STRONG>original_surface</STRONG></TT> 61</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">field 62</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">(none) 63</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">triangulated surface 64</TD></TR><TR> 65<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>max_error</STRONG></TT> 66</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">scalar 67</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">input dependent 68</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">maximum positional error 69</TD></TR><TR> 70<TD ALIGN="LEFT" VALIGN="TOP" 71WIDTH="20%"><TT><STRONG>max_data_error</STRONG></TT> 72</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">scalar 73</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">input dependent 74</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">maximum data error 75</TD></TR><TR> 76<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>volume</STRONG></TT> 77</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">flag 78</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">1 79</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">1: move vertices to preserve 80volume 81<BR> 820: do not move vertices 83</TD></TR><TR> 84<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>boundary</STRONG></TT> 85</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">flag 86</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">0 87</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">1: simplify surface boundaries 88<BR> 890: do not simplify surface boundaries 90</TD></TR><TR> 91<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>length</STRONG></TT> 92</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">flag 93</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">1 94</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">1: move vertices to preserve the 95length of boundaries 96<BR> 970: do not move vertices 98</TD></TR><TR> 99<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>data</STRONG></TT> 100</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">flag 101</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">1 102</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">1: use data dependent on 103"positions" to constrain simplification 104<BR> 1050: ignore data for simplification 106</TD></TR><TR> 107<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>stats</STRONG></TT> 108</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">flag 109</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">0 110</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">1: provide simple statistics. 111<BR> 1120: do not provide statistics 113</TD></TR></TABLE> 114<P><STRONG>Outputs</STRONG> 115<BR> 116<TABLE BORDER> 117<TR> 118<TH ALIGN="LEFT" VALIGN="TOP" WIDTH="25%">Name 119</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="25%">Type 120</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="50%">Description 121</TH></TR><TR> 122<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="25%"><TT><STRONG>simplified</STRONG></TT> 123</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="25%">field 124</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="50%">simplified triangulated surface 125</TD></TR></TABLE> 126<P><STRONG>Functional Details</STRONG> 127<P> 128SimplifySurface builds a <TT><STRONG>simplified</STRONG></TT> surface that is 129guaranteed to deviate from <TT><STRONG>original_surface</STRONG></TT> by less 130than <TT><STRONG>max_error</STRONG></TT>. This means that each vertex of 131<TT><STRONG>simplified</STRONG></TT> as well as each point inside a triangle 132of <TT><STRONG>simplified</STRONG></TT> is at a Euclidean 133distance no further than 134<TT><STRONG>max_error</STRONG></TT> from 135<TT><STRONG>original_surface</STRONG></TT>. 136Similarly, each vertex of <TT><STRONG>original_surface</STRONG></TT> as well 137as each point inside a triangle of <TT><STRONG>original_surface</STRONG></TT> 138is at a distance no further than <TT><STRONG>max_error</STRONG></TT> from the 139simplified surface. 140<P> 141In addition, if a "data" component of 142<TT><STRONG>original_surface</STRONG></TT> is dependent on the 143"positions" component and is not <TT><STRONG>TYPE_STRING</STRONG></TT>, 144SimplifySurface will perform a data dependent simplification: 145SimplifySurface will resample "data" on the simplified surface and 146guarantee that the maximum deviation between the original and re-sampled 147data is less than <TT><STRONG>max_error_data</STRONG></TT>. For efficiency 148reasons, the dimensionality of the "data" component is currently 149limited to 3: for instance, it will work for RGB colors or for gradient 150values in 3-dimension. 151Note that data dependent on connections will <B>not</B> constrain 152simplification. 153<P> 154Vertex normals for the <TT><STRONG>simplified</STRONG></TT> surface are 155automatically computed. 156<P> 157Components dependent on "positions" or "connections" of 158<TT><STRONG>original_surface</STRONG></TT> are added to 159<TT><STRONG>simplified</STRONG></TT> and re-sampled. For components dependent 160on "connections", the triangle areas are used to weight the 161resampling. 162<P> 163The following components are not re-sampled: "positions", 164"connections", "invalid positions", "invalid 165connections" "normals", "neighbors", and 166"positional error". 167<TABLE CELLPADDING="3"> 168<TR VALIGN="TOP"><TD><P><B><TT><STRONG>original_surface</STRONG></TT> 169</B></TD><TD><P>must have triangular connections. 170<TT><STRONG>original_surface</STRONG></TT> is the field that is being 171simplified. 172</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>max_error</STRONG></TT> 173</B></TD><TD><P>maximum distance 174(in the units of the "position" component) 175between <TT><STRONG>simplified</STRONG></TT> and 176<TT><STRONG>original_surface</STRONG></TT>. The default value for 177<TT><STRONG>max_error</STRONG></TT> is 1% of the diagonal of the bounding box 178of <TT><STRONG>original_surface</STRONG></TT>. You may decide to set 179<TT><STRONG>max_error</STRONG></TT> to a lower or higher value than the 180default. 181</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>max_data_error</STRONG></TT> 182</B></TD><TD><P>maximum deviation between data attached to 183<TT><STRONG>original_surface</STRONG></TT> vertices, and the resampling of 184that data on the <TT><STRONG>simplified</STRONG></TT> surface. (Again the 185maximum deviation also holds for points inside triangles, not just 186vertices). 187<P> 188The default value for the maximum error on the data is set to 10% of the 189diagonal of the bounding box in data space. If the data is one 190dimensional, the default error is (max_data-min_data)/10. 191<P> 192<TT><STRONG>max_data_error</STRONG></TT> is ignored if 193<TT><STRONG>data</STRONG></TT> = 0 or if the data are connection-dependent. 194</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>volume</STRONG></TT> 195</B></TD><TD><P>specifies whether the volume enclosed by the surface should be 196preserved or not. If set to 1, SimplifySurface will 197move the surface vertices in order to preserve the volume while the 198number of vertices is being reduced. In this case, the volume is 199preserved to within floating point or higher accuracy. If set to 0, 200the surface vertices will not be moved. The default is 1. 201<P> 202The volume is only truly defined for a surface that does not have a 203boundary (closed surface). Setting 204<TT><STRONG>volume</STRONG></TT> to 1 on a surface with boundary will have the 205effect of preventing shrinkage and producing more regular triangles. 206<P> 207Note that if several surfaces share the same boundary, as when 208Isosurface is used on partitioned data, the volume can still be 209preserved with <TT><STRONG>volume</STRONG></TT> set to 1 if the boundary is 210left intact (<TT><STRONG>boundary</STRONG></TT> set to 0). 211<P> 212With surfaces that present sharp angles, such as CAD data, setting 213<TT><STRONG>volume</STRONG></TT> to 1 might not work well. In general, we 214recommend setting <TT><STRONG>volume</STRONG></TT> to zero when operating on 215CAD data. 216</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>boundary</STRONG></TT> 217</B></TD><TD><P>specifies whether the boundary of a surface should be simplified 218or 219left intact. If set to 1, then the boundary is 220simplified while respecting the same errors 221<TT><STRONG>max_error</STRONG></TT> and 222<TT><STRONG>max_data_error</STRONG></TT>. If 223set to 0, then the boundary is left intact. The 224default is 0. If <TT><STRONG>original_surface</STRONG></TT> has no boundary, 225this option is ignored. 226</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>length</STRONG></TT> 227</B></TD><TD><P>if <TT><STRONG>boundary</STRONG></TT> set 228to 1, specifies whether the length of the simplified boundary should be 229preserved. If set to 1, in a manner analogous to 230volume preservation, SimplifySurface will move the boundary vertices in 231order to preserve the boundary length while the number of boundary 232vertices is being reduced. If set to 0, the boundary 233vertices will not be moved. The default is 1. If 234<TT><STRONG>boundary</STRONG></TT> is set to 0 then the value of 235<TT><STRONG>length</STRONG></TT> is ignored. 236</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>data</STRONG></TT> 237</B></TD><TD><P>if set to 1, instructs SimplifySurface 238use <TT><STRONG>max_data_error</STRONG></TT> to constrain simplification if 239data are dependent on "positions" and are not 240<TT><STRONG>TYPE_STRING</STRONG></TT>, and if the dimensionality of such 241data is 3 or lower. If set to 0, simplification will not be constrained 242by data. In any case, SimplifySurface will resample 243data after simplification. 244The default is 1. 245</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>stats</STRONG></TT> 246</B></TD><TD><P>if set to 1, instructs SimplifySurface to write simple 247statistics: 248number of vertices and triangles in original_surface, number of vertices 249and triangles in simplified, and percentage of original numbers of 250vertices and triangles. This information will appear in the Message window. 251If set to 0, SimplifySurface will not provide 252statistics. The default is 0. 253</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>simplified</STRONG></TT> 254</B></TD><TD><P>simplified surface. 255</TD></TR></TABLE> 256<P> 257<H4><A NAME="HDRLOD">Generating surface levels of detail.</A></H4> 258<P>SimplifySurface adds a "positional error" component to the 259<TT><STRONG>simplified</STRONG></TT> surface. "positional error" 260is a component dependent on "positions" that provides for each 261vertex of <TT><STRONG>simplified</STRONG></TT> a positive number. This 262positive number, the error value, represents 263the radius of a sphere centered on the vertex, that is guaranteed to 264intersect the original surface. The union of such spheres represents the 265error volume of the simplified surface, which is guaranteed to enclose 266the original surface. Points inside triangles are assigned an error 267value that is interpolated from the error values at the triangle 268vertices using barycentric coordinates. 269<P> 270Using the "positional error" component, a simplified surface can be 271re-simplified to any <TT><STRONG>max_error</STRONG></TT> while still 272guaranteeing a bound with respect to the original surface. This is 273useful for generating successive levels of detail. 274<P> 275If the same error bound is used, a marginal additional simplification 276can be observed: the algorithm implements a greedy method, and does not 277guarantee to find the minimum number of triangles that respects a given 278error bound. 279<P> 280The use of the "positional error" component by SimplifySurface is 281transparent to you, but you may occasionally want to visualize the 282simplification error, using the Mark module. An example is provided in 283SimplifySurface.net. 284<P><STRONG>Components</STRONG> 285<P> 286SimplifySurface adds a "positional error" component that is dependent 287on "positions" (see <A HREF="#HDRLOD">"Generating surface levels of 288detail."</A>). 289<P> 290In general <TT><STRONG>simplified</STRONG></TT> has the same components as 291<TT><STRONG>original_surface</STRONG></TT> except for "invalid positions", 292"invalid connections", "neighbors", and components that are 293<TT><STRONG>TYPE_STRING</STRONG></TT>. 294<P><STRONG>Example Visual Programs</STRONG> 295<PRE> 296SimplifySurface.net 297</PRE> 298<P><STRONG>See Also</STRONG> 299<P> 300<A HREF="refgu114.htm#HDRREFINE">Refine</A>, 301<A HREF="refgu113.htm#HDRREDUCE">Reduce</A>, 302<A HREF="refgu081.htm#HDRISOSURF">Isosurface</A>, 303<A HREF="refgu091.htm#HDRMAP">Map</A> 304 <P> 305 <HR> 306 <DIV align="center"> 307 <P><A href="../allguide.htm"><IMG src="../images/foot-fc.gif" width="94" height="18" border="0" alt="Full Contents"></A> <A href="../qikguide.htm"><IMG src="../images/foot-qs.gif" width="94" height="18" border="0" alt="QuickStart Guide"></A> <A href="../usrguide.htm"><IMG src="../images/foot-ug.gif" width="94" height="18" border="0" alt="User's Guide"></A> <A href="../refguide.htm"><IMG src="../images/foot-ur.gif" width="94" height="18" border="0" alt="User's Reference"></A></P> 308 </DIV> 309 <DIV align="center"> 310 <P><FONT size="-1">[ <A href="http://www.research.ibm.com/dx">OpenDX Home at IBM</A> | <A href="http://www.opendx.org/">OpenDX.org</A> ] </FONT></P> 311 <P></P> 312 </DIV> 313 <P></P> 314 </BODY></HTML> 315
