Usenet 1994 October/usenetsourcesnewsgroupsinfomagicoctober1994disk2.iso/misc/volume38/lic/part03

Text File | 1993-08-11 | 68KB | 2,524 lines

Newsgroups: comp.sources.misc
From: [e-mail] (Casey Leedom)
Subject: v38i106:  lic - LLNL Line Integral Convolution, v1.2, Part03/10
Message-ID: <[e-mail]>
X-Md4-Signature: f16a023797aa755cafb5cc6e192c4ca0
Sender: [e-mail] (Kent Landfield)
Organization: Sterling Software
Date: Thu, 12 Aug 1993 01:38:16 GMT
Approved: [e-mail]

Submitted-by: [e-mail] (Casey Leedom)
Posting-number: Volume 38, Issue 106
Archive-name: lic/part03
Environment: UNIX

#! /bin/sh
# This is a shell archive.  Remove anything before this line, then feed it
# into a shell via "sh file" or similar.  To overwrite existing files,
# type "sh file -c".
# Contents:  lic.1.2/doc/siggraph93/paper.ps.B
#   lic.1.2/lic/Makefile.tmpl
# Wrapped by kent@sparky on Wed Aug 11 19:38:02 1993
PATH=/bin:/usr/bin:/usr/ucb:/usr/local/bin:/usr/lbin ; export PATH
echo If this archive is complete, you will see the following message:
echo '          "shar: End of archive 3 (of 10)."'
if test -f 'lic.1.2/doc/siggraph93/paper.ps.B' -a "${1}" != "-c" ; then
  echo shar: Will not clobber existing file \"'lic.1.2/doc/siggraph93/paper.ps.B'\"
else
  echo shar: Extracting \"'lic.1.2/doc/siggraph93/paper.ps.B'\" \(60980 characters\)
  sed "s/^X//" >'lic.1.2/doc/siggraph93/paper.ps.B' <<'END_OF_FILE'
X   newpath
X   155 add moveto
X   0 95  rlineto
X   stroke
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X   grestore
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X
X0.002 setlinewidth
XSetWorld
X
X%
X% First layer
X%
X0.5 200 100                      graybox
X0                                layer      250   0  (Output image) label
X%
X% Second layer
X250                              randomlayer 250 250  (Input texture) label
X250                              outline
X%
X% Third layer
X%
X1.0 3.0 10.0 210.0 600.0         ddalayer
X1.0 3.0 210 300 div -605 300 div vector
X500                              layer      250 500  (DDA line) label
X%
X% Fourth layer
X%
X750                              layer      250 750 (Vector field) label
X1.0 3.0 210 300 div -855 300 div arrow
X
X%
X% Centerline
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X210 105         centerline
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X1 9 Q
X0 X
X0 K
X-0.04 (Only the directional component of the vector \336eld is used in this) 63 454.14 P
X0.81 (advection. The magnitude of the vector \336eld can be used later in) 54 444.14 P
X0.26 (post processing steps as explained in section 4.3.1.) 54 434.14 P
X4 F
X0.26 (D) 240.58 434.14 P
X3 F
X0.26 (s) 246.08 434.14 P
X3 7 Q
X0.2 (i) 249.57 431.89 P
X1 9 Q
X0.26 ( is the posi-) 251.52 434.14 P
X1.54 (tive parametric distance along a line parallel to the vector \336eld) 54 424.14 P
X(from) 54 414.14 T
X3 F
X(P) 73.72 414.14 T
X3 7 Q
X(i) 79.21 411.89 T
X1 9 Q
X( to the nearest cell edge.) 81.15 414.14 T
X0.16 (As with the DDA algorithm, it is important to maintain symme-) 63 404.12 P
X0.03 (try about a cell. Hence, the local stream line is also advected back-) 54 394.12 P
X(wards by the negative of the vector \336eld as shown in equation \0503\051.) 54 384.12 T
X-0.12 (Primed variables represent the negative direction counterparts to) 63 327.05 P
X0.35 (the positive direction variables and are not repeated in subsequent) 54 317.05 P
X(de\336nitions. As above) 54 307.05 T
X4 F
X(D) 132.39 307.05 T
X3 F
X(s\325) 137.89 307.05 T
X3 7 Q
X(i) 144.38 304.8 T
X1 9 Q
X(, is always positive.) 146.32 307.05 T
X-0.03 (The calculation of) 63 297.03 P
X4 F
X-0.03 (D) 130.54 297.03 P
X3 F
X-0.03 (s) 136.04 297.03 P
X3 7 Q
X-0.03 (i) 139.54 294.78 P
X1 9 Q
X-0.03 ( in the stream line advection is sensitive to) 141.48 297.03 P
X1.34 (round of) 54 287.03 P
X1.34 (f errors.) 85.88 287.03 P
X4 F
X1.34 (D) 119.26 287.03 P
X3 F
X1.34 (s) 124.76 287.03 P
X3 7 Q
X1.04 (i) 128.25 284.78 P
X1 9 Q
X1.34 ( must produce advected coordinates that lie) 130.2 287.03 P
X0.09 (within the) 54 277.03 P
X3 F
X0.09 (i) 92.63 277.03 P
X1 F
X0.09 (+1) 95.13 277.03 P
X1 7 Q
X0.07 (th) 104.69 280.63 P
X1 9 Q
X0.09 ( cell, taking the stream line segment out of the cur-) 110.13 277.03 P
X0.27 (rent cell. In the implementation of the algorithm a small round of) 54 267.03 P
X0.27 (f) 291.01 267.03 P
X0.28 (term is added to each) 54 257.03 P
X4 F
X0.28 (D) 134.03 257.03 P
X3 F
X0.28 (s) 139.53 257.03 P
X3 7 Q
X0.22 (i) 143.03 254.78 P
X1 9 Q
X0.28 ( to insure that entry into the adjacent cell) 144.97 257.03 P
X0.49 (occurs. This local stream line calculation is illustrated in \336gure 3.) 54 247.03 P
X-0.18 (Each cell is assumed to be a unit square. All spatial quantities \050e.g.,) 54 237.03 P
X4 F
X0.48 (D) 54 227.03 P
X3 F
X0.48 (s) 59.5 227.03 P
X3 7 Q
X0.37 (i) 63 224.78 P
X1 9 Q
X0.48 (\051 are relative to this measurement. However) 64.94 227.03 P
X0.48 (, the cells need not) 224.94 227.03 P
X0.84 (be square or even rectangular \050see section 6\051 for this approxima-) 54 217.03 P
X0.32 (tion to work. So, without loss of generality) 54 207.03 P
X0.32 (, descriptions are given) 209.68 207.03 P
X(relative to a cubic lattice with unit spacing.) 54 197.03 T
X0.68 (Continuous sections of the local stream line \321 i.e. the straight) 63 187 P
X1.15 (line segments in \336gure 3 \321 can be thought of as parameterized) 54 177 P
X0.51 (space curves in) 54 167 P
X3 F
X0.51 (s) 112.68 167 P
X1 F
X0.51 ( and the input texture pixel mapped to a cell can) 116.18 167 P
X1.11 (be treated as a continuous scalar function of x and y) 54 157 P
X1.11 (.) 251.22 157 P
X1 7 Q
X0.86 (2) 253.47 160.6 P
X1 9 Q
X1.11 ( It is then) 256.96 157 P
X-0.15 (possible to integrate over this scalar \336eld along each parameterized) 54 147 P
X-0.14 (space curve. Such integrals can be summed in a piecewise) 54 137 P
X2 F
X-0.14 (C) 263.95 137 P
X2 7 Q
X-0.11 (1) 270.44 140.6 P
X1 9 Q
X-0.14 ( fash-) 273.93 137 P
X0.01 (ion and are known as line integrals of the \336rst kind \050LIFK\051[2]. The) 54 127 P
X0.29 (convolution concept used in the DDA algorithm can now be com-) 54 117 P
X54 99 294 114 C
X63 112 207 112 2 L
X0.5 H
X2 Z
X0 X
X0 K
XN
X0 0 612 792 C
X1 6 Q
X0 X
X0 K
X0.78 (2.) 54 96.87 P
X1 8 Q
X1.04 (Bilinear) 60.78 93.67 P
X1.04 (, cubic or Bezier splines are viable alternatives to straight line) 86.22 93.67 P
X0.19 (segments. However) 54 84.67 P
X0.19 (, these higher order curves are more expensive to com-) 116.93 84.67 P
X(pute.) 54 75.67 T
X54 72 294 460.14 C
X54 334.08 294 381.12 C
X3 9 Q
X0 X
X0 K
X(P) 82.33 350.08 T
X1 F
X(') 88.32 350.08 T
X3 7 Q
X(i) 91.17 346.95 T
X3 9 Q
X(P) 107.04 350.08 T
X1 F
X(') 113.04 350.08 T
X3 7 Q
X(i) 115.88 346.95 T
X1 F
X(1) 125.16 346.95 T
X4 F
X(-) 119.57 346.95 T
X3 9 Q
X(V) 144.84 358.67 T
X(P) 162.25 358.67 T
X1 F
X(') 168.24 358.67 T
X3 7 Q
X(i) 171.08 355.54 T
X1 F
X(1) 180.36 355.54 T
X4 F
X(-) 174.78 355.54 T
X4 9 Q
X(\050) 152.36 358.67 T
X(\051) 190.25 358.67 T
X3 F
X(V) 144.84 343.88 T
X(P) 162.25 343.88 T
X1 F
X(') 168.24 343.88 T
X3 7 Q
X(i) 171.08 340.75 T
X1 F
X(1) 180.36 340.75 T
X4 F
X(-) 174.78 340.75 T
X4 9 Q
X(\050) 152.36 343.88 T
X(\051) 190.25 343.88 T
X(D) 202.02 350.08 T
X3 F
X(s) 208.05 350.08 T
X1 F
X(') 212.05 350.08 T
X3 7 Q
X(i) 214.89 346.95 T
X1 F
X(1) 224.17 346.95 T
X4 F
X(-) 218.59 346.95 T
X4 9 Q
X(-) 130.9 350.08 T
X(=) 97.61 350.08 T
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X0.33 H
X0 Z
XN
X157.25 355.03 160.25 355.03 2 L
XN
X187.86 355.03 187.86 364.82 2 L
XN
X187.86 355.03 184.86 355.03 2 L
XN
X157.25 340.23 157.25 350.03 2 L
XN
X157.25 340.23 160.25 340.23 2 L
XN
X187.86 340.23 187.86 350.03 2 L
XN
X187.86 340.23 184.86 340.23 2 L
XN
X139.84 340.23 139.84 350.03 2 L
XN
X141.84 340.23 141.84 350.03 2 L
XN
X198.74 340.23 198.74 350.03 2 L
XN
X196.74 340.23 196.74 350.03 2 L
XN
X138.84 352.03 200.49 352.03 2 L
XN
X3 F
X(P) 82.33 371.95 T
X1 F
X(') 88.32 371.95 T
X1 7 Q
X(0) 91.17 368.83 T
X3 9 Q
X(P) 108.6 371.95 T
X1 7 Q
X(0) 114.43 368.83 T
X4 9 Q
X(=) 99.16 371.95 T
X271.88 354.33 294.02 365.05 R
X7 X
XV
X1 F
X0 X
X(\0503\051) 271.88 359.05 T
X54 72 294 460.14 C
X0 0 612 792 C
X1 9 Q
X0 X
X0 K
X0.51 (bined with LIFK to form a Line Integral Convolution \050LIC\051. This) 317.29 732 P
X0.19 (results in a variation of the DDA approach that locally follows the) 317.29 722 P
X1.38 (vector \336eld and captures small radius of curvature features. For) 317.29 712 P
X0.09 (each continuous segment,) 317.29 702 P
X3 F
X0.09 (i) 412.4 702 P
X1 F
X0.09 (, an exact integral of a convolution ker-) 414.9 702 P
X0.31 (nel) 317.29 692 P
X3 F
X0.31 (k) 330.83 692 P
X1 F
X0.31 (\050) 334.82 692 P
X3 F
X0.31 (w) 337.81 692 P
X1 F
X0.31 (\051 is computed and used as a weight in the LIC as shown in) 343.8 692 P
X(equation \0504\051.) 317.29 682 T
X0.03 (The entire LIC for output pixel) 326.29 595.27 P
X3 F
X0.03 (F\325\050x, y\051) 440.29 595.27 P
X1 F
X0.03 ( is given by equation \0505\051.) 467.27 595.27 P
X-0.17 (The numerator of equation \0505\051 represents the line integral of the \336l-) 317.29 465.27 P
X-0.08 (ter kernel times the input pixel \336eld,) 317.29 455.27 P
X3 F
X-0.08 (F) 449.55 455.27 P
X1 F
X-0.08 (. The denominator is the line) 454.33 455.27 P
X0.01 (integral of the convolution kernel and is used to normalize the out-) 317.29 445.27 P
X(put pixel weight \050see section 4.2\051.) 317.29 435.27 T
X0.8 (The length of the local stream line,) 326.29 422.7 P
X3 F
X0.8 (2L) 459.67 422.7 P
X1 F
X0.8 (, is given in unit pixels.) 469.16 422.7 P
X1.67 (Depending on the input pixel \336eld,) 317.29 412.7 P
X3 F
X1.67 (F) 454.87 412.7 P
X1 F
X1.67 (, if) 459.64 412.7 P
X3 F
X1.67 (L) 475.21 412.7 P
X1 F
X1.67 ( is too lar) 480.2 412.7 P
X1.67 (ge, all the) 518.75 412.7 P
X0.04 (resulting LICs will return values very close together for all coordi-) 317.29 402.7 P
X-0.02 (nates \050) 317.29 392.7 P
X3 F
X-0.02 (x) 340.98 392.7 P
X1 F
X-0.02 (,) 344.97 392.7 P
X3 F
X-0.02 (y) 349.45 392.7 P
X1 F
X-0.02 (\051. On the other hand, if) 353.44 392.7 P
X3 F
X-0.02 (L) 437.7 392.7 P
X1 F
X-0.02 ( is too small then an insuf) 442.7 392.7 P
X-0.02 (\336cient) 534.82 392.7 P
X2.59 (amount of \336ltering occurs. Since the value of) 317.29 382.7 P
X3 F
X2.59 (L) 502.52 382.7 P
X1 F
X2.59 ( dramatically) 507.52 382.7 P
X1.81 (af) 317.29 372.7 P
X1.81 (fects the performance of the algorithm, the smallest ef) 324.11 372.7 P
X1.81 (fective) 532.83 372.7 P
X(value is desired. For most of the \336gures, a value of 10 was used.) 317.29 362.7 T
X0.28 (Singularities in the vector \336eld occur when vectors in two adja-) 326.29 350.14 P
X0.84 (cent local stream line cells geometrically \322point\323 at a shared cell) 317.29 340.14 P
X0.39 (edge. This results in) 317.29 330.14 P
X4 F
X0.39 ( D) 390.84 330.14 P
X3 F
X0.39 (s) 398.98 330.14 P
X3 7 Q
X0.3 (i) 402.47 327.89 P
X1 9 Q
X0.39 ( values equal to zero leaving) 404.42 330.14 P
X3 F
X0.39 (l) 511.57 330.14 P
X1 F
X0.39 ( in equation) 514.07 330.14 P
X0.26 (\0506\051 unde\336ned. This situation can easily be detected and the advec-) 317.29 320.14 P
X1.08 (tion algorithm terminated. If the vector \336eld goes to zero at any) 317.29 310.14 P
X0.26 (point, the LIC algorithm is terminated as in the case of a \336eld sin-) 317.29 300.14 P
X0.85 (gularity) 317.29 290.14 P
X0.85 (. Both of these cases generate truncated stream lines. If a) 344.66 290.14 P
X0.3 (zero \336eld vector lies in the starting cell of the LIC, the input pixel) 317.29 280.14 P
X0.85 (value for that cell, a constant or any other arbitrary value can be) 317.29 270.14 P
X1.39 (returned as the value of the LIC depending on the visual ef) 317.29 260.14 P
X1.39 (fect) 543.81 260.14 P
X(desired for null vectors.) 317.29 250.14 T
X1.23 ( Using adjacent stream line vectors to detect singularities can) 326.29 237.57 P
X-0.17 (however result in false singularities. False singularities occur when) 317.29 227.57 P
X0.3 (the vector \336eld is nearly parallel to an edge, but causes the LIC to) 317.29 217.57 P
X0.12 (cross over that edge. Similarly) 317.29 207.57 P
X0.12 (, the cell just entered also has a near) 426.77 207.57 P
X0.16 (parallel vector which points to this same shared edge. This artifact) 317.29 197.57 P
X0.09 (can be remedied by adjusting the parallel vector/edge test found in) 317.29 187.57 P
X0.76 (equation \0502\051, to test the angle formed between the vector and the) 317.29 177.57 P
X0.84 (edge against some small angle) 317.29 167.57 P
X3 F
X0.84 (theta) 433.05 167.57 P
X1 F
X0.84 (, instead of zero. Any vector) 451.02 167.57 P
X0.2 (which forms an angle less than) 317.29 157.57 P
X3 F
X0.2 (theta) 431.79 157.57 P
X1 F
X0.2 ( with some edge is deemed to) 449.77 157.57 P
X0.88 (be \322parallel\323 to that edge. Using a value of 3) 317.29 147.57 P
X4 F
X0.88 (\260) 485.42 147.57 P
X1 F
X0.88 ( for) 489.01 147.57 P
X3 F
X0.88 (theta) 505.74 147.57 P
X1 F
X0.88 ( removes) 523.71 147.57 P
X(these artifacts.) 317.29 137.57 T
X0.09 (The images in \336gure 4 were rendered using LIC and correspond) 326.29 125 P
X2.62 (to the same two vector \336elds rendered in \336gure 2. Note the) 317.29 115 P
X1.68 (increased amount of detail present in these images versus their) 317.29 105 P
X1.04 (DDA counterparts. In particular the image of the \337uid dynamics) 317.29 95 P
X0.34 (vector \336eld in \336gure 4 shows detail incorrectly rendered or absent) 317.29 85 P
X(in \336gure 2.) 317.29 75 T
X317.29 72 557.29 738 C
X317.3 604.84 557.27 679 C
X3 9 Q
X0 X
X0 K
X(h) 347.73 654.15 T
X3 7 Q
X(i) 352.57 651.02 T
X3 9 Q
X(k) 390.35 654.15 T
X(w) 400.26 654.15 T
X4 F
X(\050) 396.37 654.15 T
X(\051) 406.64 654.15 T
X3 F
X(d) 411.67 654.15 T
X(w) 416.69 654.15 T
X3 7 Q
X(s) 376.71 641.16 T
X3 5 Q
X(i) 379.7 638.91 T
X3 7 Q
X(s) 368.45 669.02 T
X3 5 Q
X(i) 371.44 666.78 T
X4 7 Q
X(D) 380.16 669.02 T
X3 F
X(s) 384.98 669.02 T
X3 5 Q
X(i) 387.96 666.78 T
X4 7 Q
X(+) 374.57 669.02 T
X4 14 Q
X(\362) 376.98 650.43 T
X4 9 Q
X(=) 359.02 654.15 T
X1 F
X(w) 330.07 634.77 T
X(h) 336.56 634.77 T
X(e) 341.05 634.77 T
X(r) 345.05 634.77 T
X(e) 348.04 634.77 T
X3 F
X(s) 347.73 627.36 T
X1 7 Q
X(0) 351.58 624.24 T
X1 9 Q
X(0) 369 627.36 T
X4 F
X(=) 359.57 627.36 T
X3 F
X(s) 347.11 614.27 T
X3 7 Q
X(i) 350.95 611.14 T
X3 9 Q
X(s) 369.1 614.27 T
X3 7 Q
X(i) 372.94 611.14 T
X1 F
X(1) 382.22 611.14 T
X4 F
X(-) 376.64 611.14 T
X4 9 Q
X(D) 395.15 614.27 T
X3 F
X(s) 401.18 614.27 T
X3 7 Q
X(i) 405.02 611.14 T
X1 F
X(1) 414.3 611.14 T
X4 F
X(-) 408.72 611.14 T
X4 9 Q
X(+) 387.97 614.27 T
X(=) 359.67 614.27 T
X536.87 649.92 559.01 660.64 R
X7 X
XV
X1 F
X0 X
X(\0504\051) 536.87 654.64 T
X317.29 72 557.29 738 C
X0 0 612 792 C
X317.29 72 557.29 738 C
X317.3 474.01 557.27 592.27 C
X3 9 Q
X0 X
X0 K
X(F) 347.73 553.79 T
X1 F
X(') 353.72 553.79 T
X3 F
X(x) 362.14 553.79 T
X(y) 370.63 553.79 T
X4 F
X(,) 366.13 553.79 T
X(\050) 358.25 553.79 T
X(\051) 375.01 553.79 T
X3 F
X(F) 409.13 570.1 T
X(P) 426.53 570.1 T
X3 7 Q
X(i) 432.37 566.97 T
X4 9 Q
X(\050) 416.65 570.1 T
X(\051) 440.71 570.1 T
X3 F
X(h) 445.73 570.1 T
X3 7 Q
X(i) 450.57 566.97 T
X3 9 Q
X(F) 476.89 570.1 T
X(P) 494.29 570.1 T
X1 F
X(') 500.28 570.1 T
X3 7 Q
X(i) 503.13 566.97 T
X4 9 Q
X(\050) 484.41 570.1 T
X(\051) 511.46 570.1 T
X3 F
X(h) 516.49 570.1 T
X1 F
X(') 521.48 570.1 T
X3 7 Q
X(i) 524.33 566.97 T
X(i) 461.95 558.25 T
X1 F
X(0) 472.39 558.25 T
X4 F
X(=) 466.22 558.25 T
X3 F
X(l) 466.44 582 T
X1 F
X(') 468.89 582 T
X4 14 Q
X(\345) 463.93 567.54 T
X4 9 Q
X(+) 454.76 570.1 T
X3 7 Q
X(i) 394.19 558.25 T
X1 F
X(0) 404.63 558.25 T
X4 F
X(=) 398.46 558.25 T
X3 F
X(l) 400.18 582 T
X4 14 Q
X(\345) 396.17 567.54 T
X3 9 Q
X(h) 447.23 537.55 T
X3 7 Q
X(i) 452.07 534.42 T
X3 9 Q
X(h) 478.39 537.55 T
X1 F
X(') 483.38 537.55 T
X3 7 Q
X(i) 486.23 534.42 T
X(i) 463.45 525.7 T
X1 F
X(0) 473.89 525.7 T
X4 F
X(=) 467.72 525.7 T
X3 F
X(l) 467.94 549.45 T
X1 F
X(') 470.39 549.45 T
X4 14 Q
X(\345) 465.43 534.99 T
X4 9 Q
X(+) 456.26 537.55 T
X3 7 Q
X(i) 432.29 525.7 T
X1 F
X(0) 442.73 525.7 T
X4 F
X(=) 436.56 525.7 T
X3 F
X(l) 438.29 549.45 T
X4 14 Q
X(\345) 434.27 534.99 T
X4 9 Q
X(=) 384 553.79 T
X421.53 566.53 421.53 576.25 2 L
X0.33 H
X0 Z
XN
X421.53 566.53 424.53 566.53 2 L
XN
X438.31 566.53 438.31 576.25 2 L
XN
X438.31 566.53 435.31 566.53 2 L
XN
X489.29 566.53 489.29 576.25 2 L
XN
X489.29 566.53 492.29 566.53 2 L
XN
X509.07 566.53 509.07 576.25 2 L
XN
X509.07 566.53 506.07 566.53 2 L
XN
X394.19 555.73 526.02 555.73 2 L
XN
X1 F
X(w) 328.41 519.37 T
X(h) 334.9 519.37 T
X(e) 339.39 519.37 T
X(r) 343.38 519.37 T
X(e) 346.37 519.37 T
X3 F
X(F) 347.13 508.86 T
X(P) 364.54 508.86 T
X4 F
X(\050) 354.65 508.86 T
X(\051) 376.42 508.86 T
X1 F
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X0.396695 0.917951 2 4 arrow
X0.345008 0.938600 2 5 arrow
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Xgrestore
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X
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X612 792 0 FMBEGINPAGE
X1 9 Q
X0 X
X0 K
X0.61 (The images in \336gure 5 show the ef) 63 586.29 P
X0.61 (fect of varying) 191.63 586.29 P
X3 F
X0.61 (L) 248.6 586.29 P
X1 F
X0.61 (. The input) 253.6 586.29 P
X0.4 (texture is a photograph of \337owers. The input vector \336eld was cre-) 54 576.27 P
X0.06 (ated by taking the gradient of a bandlimited noise image and rotat-) 54 566.26 P
X0.75 (ing each of the gradient vectors by 90) 54 556.24 P
X4 F
X0.75 (\260) 194.8 556.24 P
X1 F
X0.75 (, producing vectors which) 198.39 556.24 P
X0.24 (follow the contours of the soft hills and valleys of the bandlimited) 54 546.23 P
X2.63 (noise) 54 536.21 P
X4 F
X2.63 (.) 72.97 536.21 P
X1 F
X2.63 ( W) 75.22 536.21 P
X2.63 (ith) 88.22 536.21 P
X3 F
X2.63 (L) 102.58 536.21 P
X1 F
X2.63 ( equal to 0, the input image is passed through) 107.58 536.21 P
X0.24 (unchanged. As the value of) 54 526.2 P
X3 F
X0.24 (L) 155.53 526.2 P
X1 F
X0.24 ( increases, the input image is blurred) 160.52 526.2 P
X0.26 (to a greater extent, giving an impressionistic result. Here, a biased) 54 516.19 P
X(ramp \336lter[10] is used to roughly simulate a brush stroke.) 54 506.17 T
X0.12 (Figures 2, 4, 8, 9 and 1) 63 493.17 P
X0.12 (1 were generated using white noise input) 146.01 493.17 P
X0.31 (images. Aliasing can be a serious problem when using LIC with a) 54 483.16 P
X0.71 (high frequency source image such as white noise. The aliasing is) 54 473.14 P
X-0.1 (caused by the one-dimensional point sampling of the in\336nitely thin) 54 463.13 P
X0.49 (LIC \336lter) 54 453.11 P
X0.49 (. This aliasing can be removed by either creating a thick) 87.7 453.11 P
X0.24 (LIC \336lter with a low-pass \336lter cross section or by low-pass \336lter-) 54 443.1 P
X0.76 (ing the input image. This second alternative is preferable since it) 54 433.09 P
X0.94 (comes at no additional cost to the LIC algorithm. The images in) 54 423.07 P
X0.3 (\336gure 6 show the ef) 54 413.06 P
X0.3 (fect of running LIC over 256x256 white noise) 126.42 413.06 P
X0.4 (which has been low-pass \336ltered using a fourth order Butterworth) 54 403.04 P
X(\336lter with cutof) 54 393.03 T
X(f frequencies of 128, 84, 64, and 32.) 109.76 393.03 T
X0.57 (It is worth noting that V) 63 380.03 P
X0.57 (an W) 151.48 380.03 P
X0.57 (ijk\325) 170.9 380.03 P
X0.57 (s spot noise algorithm[23] can) 182.89 380.03 P
X1.83 (be adapted to use the local stream line approximation to more) 54 370.02 P
X2.43 (accurately represent the behavior of a vector \336eld. Instead of) 54 360 P
X0.01 (straight line elliptical stretching, each spot could be warped so that) 317.29 732 P
X2.23 (the major axis follows the local stream line. Furthermore, the) 317.29 722 P
X0.34 (minor axis could either be perpendicular to the warped major axis) 317.29 712 P
X0.22 (or itself could be warped along transverse \336eld lines. However) 317.29 702 P
X0.22 (, an) 544.08 702 P
X1.43 (algorithm to perform this task for an arbitrary local stream line) 317.29 692 P
X1.46 (would be inherently more expensive and complex than the LIC) 317.29 682 P
X(algorithm.) 317.29 672 T
X2.56 (Sims[18] describes an alternative technique which produces) 326.29 660.75 P
X0.54 (results similar to LIC. This alternative approach warps or advects) 317.29 650.75 P
X0.91 (texture coordinates as a function of a vector \336eld. The similarity) 317.29 640.75 P
X1.12 (between the two techniques is predictable even though the tech-) 317.29 630.75 P
X0.48 (niques are quite dif) 317.29 620.75 P
X0.48 (ferent. The dilation and contraction of the tex-) 387.7 620.75 P
X1.36 (ture coordinate system warping has the visual ef) 317.29 610.75 P
X1.36 (fect of blurring) 500.15 610.75 P
X1.06 (and sharpening the warped image. This is due to the resampling) 317.29 600.75 P
X2.66 (and reconstruction process necessary when warping from one) 317.29 590.75 P
X0.85 (coordinate system to another) 317.29 580.75 P
X0.85 (. Thus, for regions where the source) 422.92 580.75 P
X0.54 (image is stretched along the vector \336eld an apparent blurring will) 317.29 570.75 P
X0.27 (occur similar to those seen with LIC. However) 317.29 560.75 P
X0.27 (, the techniques are) 487.08 560.75 P
X0 (completely dif) 317.29 550.75 P
X0 (ferent in two fundamental ways. First, LIC is a local) 369.3 550.75 P
X-0.1 (operator) 317.29 540.75 P
X-0.1 (, meaning no information outside of a \336xed area of interest) 346.87 540.75 P
X0.92 (is needed. W) 317.29 530.75 P
X0.92 (arping even when done locally requires maintaining) 365.07 530.75 P
X1.76 (global consistency to avoid tearing holes in the warped image.) 317.29 520.75 P
X-0.04 (This increases the complexity of the warping operation when com-) 317.29 510.75 P
X0.04 (pared to LIC. Second, LIC is a spatially varying \336ltering operation) 317.29 500.75 P
X(and does not warp or transform any texture coordinates.) 317.29 490.75 T
X0 F
X(4.1  PERIODIC MOTION FIL) 317.29 472.5 T
X(TERS) 431.98 472.5 T
X1 F
X0.09 (The LIC algorithm visualizes local vector \336eld tangents, but not) 326.29 461.25 P
X0.07 (their direction. Freeman, et al[8] describe a technique which simu-) 317.29 451.25 P
X0.11 (lates motion by use of special convolutions. A similar technique is) 317.29 441.25 P
X0.9 (used by V) 317.29 431.25 P
X0.9 (an Gelder and W) 354.54 431.25 P
X0.9 (ilhelms[22] to show vector \336eld \337ow) 418.04 431.25 P
X0.9 (.) 555.04 431.25 P
X-0.21 (This technique can be extended and used to represent the local vec-) 317.29 421.25 P
X0.68 (tor \336eld direction via animation of successive LIC imaged vector) 317.29 411.25 P
X(\336elds using varying phase shifted periodic \336lter kernels.) 317.29 401.25 T
X0.26 (The success of this technique depends on the shape of the \336lter) 326.29 390 P
X0.26 (.) 555.04 390 P
X0.26 (In the previous examples \050\336gures 2 and 4\051, a constant or box \336lter) 317.29 380 P
X-0.01 (is used. If the \336lter is periodic like the \336lters used in [8], by chang-) 317.29 370 P
X0.18 (ing the phase of such \336lters as a function of time, apparent motion) 317.29 360 P
X54 598.46 293.98 738 C
X54 598.46 293.98 738 R
X7 X
X0 K
XV
X54 598.46 293.98 616.46 R
XV
X5 8 Q
X0 X
X(Figur) 54 611.13 T
X(e 4: Cir) 72.09 611.13 T
X(cular and turbulent \337uid dynamics vector \336elds) 98.82 611.13 T
X(imaged using LIC over white noise.) 54 602.13 T
X54.72 621.72 293.26 737.28 R
X7 X
XV
X0.1 H
X2 Z
X14 X
XN
X0 0 612 792 C
X54 90 293.98 352.51 C
X54 90 293.98 352.51 R
X7 X
X0 K
XV
X54 90 293.98 108 R
XV
X5 8 Q
X0 X
X(Figur) 54 102.67 T
X(e 5: Photograph of \337owers pr) 72.09 102.67 T
X(ocessed using LIC with) 183.43 102.67 T
X6 F
X(L) 272.42 102.67 T
X5 F
X(equal to 0, 5, 10 and 20 \050left to right, top to bottom\051.) 54 93.67 T
X54.72 113.26 293.26 351.79 R
X7 X
XV
X0.1 H
X2 Z
X14 X
XN
X0 0 612 792 C
X317.3 72 557.28 352.51 C
X317.3 72 557.28 352.51 R
X7 X
X0 K
XV
X317.3 72 557.28 108 R
XV
X5 8 Q
X0 X
X(Figur) 317.3 102.67 T
X(e 6: The upper left hand quarter of the cir) 335.4 102.67 T
X(cular vector) 494.89 102.67 T
X(\336eld is convolved using LIC over Butterworth low-pass \336lter) 317.3 93.67 T
X(ed) 540.02 93.67 T
X(white noise with cutof) 317.3 84.67 T
X(f fr) 401.34 84.67 T
X(equencies of 128, 86, 64, and 32 \050left) 410.95 84.67 T
X(to right, top to bottom\051.) 317.3 75.67 T
X318.02 113.26 556.56 351.79 R
X7 X
XV
X0.1 H
X2 Z
X14 X
XN
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X612 792 0 FMBEGINPAGE
X1 9 Q
X0 X
X0 K
X0.73 (in the direction of the vector \336eld is created. However) 54 732 P
X0.73 (, the \336lters) 254.35 732 P
X0.85 (used in [8] were, by design, high-pass Laplacian edge enhancing) 54 722 P
X0.7 (\336lters. Using this \336lter over a bandlimited noise texture produces) 54 712 P
X1.3 (very incoherent images since the high frequency components of) 54 702 P
X0.64 (the noise are accentuated. Instead, it is possible, and desirable, to) 54 692 P
X-0.01 (create periodic low-pass \336lters to blur the underlying texture in the) 54 682 P
X0.75 (direction of the vector \336eld. A Hanning \336lter) 54 672 P
X3 F
X0.75 (,) 219.51 672 P
X1 F
X0.75 (1/2\0501 + cos\050) 224.76 672 P
X3 F
X0.75 (w) 269.77 672 P
X1 F
X0.75 (+) 275.76 672 P
X4 F
X0.75 (b) 280.83 672 P
X1 F
X0.75 (\051\051,) 285.77 672 P
X1.19 (has this property) 54 662 P
X1.19 (. It has low band-pass \336lter characteristics, it is) 115.71 662 P
X0.86 (periodic by de\336nition and has a simple analytic form. This func-) 54 652 P
X(tion will be referred to as the) 54 642 T
X3 F
X(ripple) 160.08 642 T
X1 F
X( \336lter function.) 181.55 642 T
X0.81 (Since the LIC algorithm is by de\336nition a local operation, any) 63 630.98 P
X0.36 (\336lter used must be windowed. That is, it must be made local even) 54 620.98 P
X0.43 (if it has in\336nite extent. In the previous section we used a constant) 54 610.98 P
X0.12 (\336lter implicitly windowed by a box of height one. Using this same) 54 600.98 P
X0.53 (box window on a phase shifted Hanning \336lter we get a \336lter with) 54 590.98 P
X(abrupt cutof) 54 580.98 T
X(fs, as illustrated in the top row of \336gure 7.) 97.52 580.98 T
X1.25 (This abrupt cutof) 63 569.96 P
X1.25 (f is noticeable as spatio-temporal artifacts in) 127.25 569.96 P
X0.35 (animations that vary the phase as a function of time. One solution) 54 559.96 P
X2.05 (to this problem is to use a Gaussian window as suggested by) 54 549.96 P
X1.26 (Gabor[4].) 54 539.96 P
X1 7 Q
X0.98 (3) 89.19 543.56 P
X1 9 Q
X1.26 ( By multiplying, or windowing, the Hanning function) 92.68 539.96 P
X-0.05 (by a Gaussian, these cutof) 54 529.96 P
X-0.05 (fs are smoothly attenuated to zero. How-) 147.76 529.96 P
X-0 (ever) 54 519.96 P
X-0 (, a Gaussian windowed Hanning function does not have a sim-) 69.11 519.96 P
X1.61 (ple closed form integral. An alternative is to \336nd a windowing) 54 509.96 P
X2.23 (function with windowing properties similar to a Gaussian and) 54 499.96 P
X-0.14 (which has a simple closed form integral. Interestingly) 54 489.96 P
X-0.14 (, the Hanning) 245.61 489.96 P
X0.03 (function itself meets these two criteria. In the bottom row of \336gure) 54 479.96 P
X0.09 (7, the \336ve phase shifted Hanning \336lter functions in the top row are) 54 469.96 P
X-0.18 (multiplied by the Hanning window function in the middle row) 54 459.96 P
X-0.18 (. The) 275.71 459.96 P
X-0.16 (general form of this function is shown in equation \0507\051. In this equa-) 54 449.96 P
X0.83 (tion) 54 389.96 P
X3 F
X0.83 (c) 71.06 389.96 P
X1 F
X0.83 ( and) 75.05 389.96 P
X3 F
X0.83 (d) 94.18 389.96 P
X1 F
X0.83 ( represent the dilation constants of the Hanning win-) 98.67 389.96 P
X2.11 (dow and ripple functions respectively) 54 379.96 P
X2.11 (.) 197.14 379.96 P
X4 F
X2.11 (b) 203.74 379.96 P
X1 F
X2.11 ( is the ripple function) 208.68 379.96 P
X0.34 (phase shift given in radians. The integral of) 54 369.96 P
X3 F
X0.34 (k) 215.19 369.96 P
X1 F
X0.34 (\050) 219.18 369.96 P
X3 F
X0.34 (w) 222.17 369.96 P
X1 F
X0.34 (\051 from) 228.17 369.96 P
X3 F
X0.34 (a) 253.8 369.96 P
X1 F
X0.34 ( to) 258.29 369.96 P
X3 F
X0.34 (b) 270.45 369.96 P
X1 F
X0.34 ( used) 274.94 369.96 P
X(in equation \0504\051 is shown in equation \0508\051.) 54 359.96 T
X1.15 (As mentioned above, both the Hanning window and the Han-) 63 205.02 P
X0.68 (ning ripple \336lter function can be independently dilated by adjust-) 54 195.02 P
X1.72 (ing) 54 185.02 P
X3 F
X1.72 (c) 69.45 185.02 P
X1 F
X1.72 ( and) 73.44 185.02 P
X3 F
X1.72 (d) 94.36 185.02 P
X1 F
X1.72 ( to have speci\336c local support and periodicity) 98.85 185.02 P
X1.72 (. The) 273.81 185.02 P
X(window function has a \336xed period of 2) 54 175.02 T
X4 F
X(p) 197.53 175.02 T
X1 F
X(.) 202.46 175.02 T
X0.54 (Choosing the periodicity of the ripple function represents mak-) 63 164 P
X0.81 (ing a design trade-of) 54 154 P
X0.81 (f between maintaining a nearly constant fre-) 130.4 154 P
X0.24 (quency response as a function of phase shift and the quality of the) 54 144 P
X54 126 294 141 C
X63 139 207 139 2 L
X0.5 H
X2 Z
X0 X
X0 K
XN
X0 0 612 792 C
X1 6 Q
X0 X
X0 K
X1.27 (3.) 54 123.87 P
X1 8 Q
X1.7 (D. Gabor in 1946 created a localized form of the Fourier transform) 61.27 120.67 P
X0.46 (known as the Gabor transform. This transform is the Fourier transform of) 54 111.67 P
X0.44 (an input signal multiplied by a Gaussian window translated along the sig-) 54 102.67 P
X0.6 (nal as a function of time. The net result is a signal which is spatially and) 54 93.67 P
X1.22 (frequency localized. W) 54 84.67 P
X1.22 (avelet theory is based on a generalization of this) 130.17 84.67 P
X(type of spatial and frequency localization.) 54 75.67 T
X54 72 294 738 C
X54.01 397.28 293.99 446.96 C
X3 9 Q
X0 X
X0 K
X(k) 85.01 429.19 T
X(w) 94.92 429.19 T
X4 F
X(\050) 91.03 429.19 T
X(\051) 101.31 429.19 T
X1 F
X(1) 120.48 436.12 T
X3 F
X(c) 153.31 436.12 T
X(w) 157.83 436.12 T
X4 F
X(\050) 149.42 436.12 T
X(\051) 164.21 436.12 T
X1 F
X(c) 134.94 436.12 T
X(o) 138.93 436.12 T
X(s) 143.43 436.12 T
X4 F
X(+) 127.23 436.12 T
X1 F
X(2) 142.35 423 T
X(1) 179.64 436.12 T
X3 F
X(d) 212.46 436.12 T
X(w) 217.49 436.12 T
X4 F
X(b) 232.91 436.12 T
X(+) 225.73 436.12 T
X(\050) 208.58 436.12 T
X(\051) 238.24 436.12 T
X1 F
X(c) 194.1 436.12 T
X(o) 198.09 436.12 T
X(s) 202.58 436.12 T
X4 F
X(+) 186.38 436.12 T
X1 F
X(2) 208.94 423 T
X4 F
X(\264) 171.71 429.19 T
X(=) 110.3 429.19 T
X120.48 431.13 168.46 431.13 2 L
X0.33 H
X0 Z
XN
X179.64 431.13 242.49 431.13 2 L
XN
X1 F
X(\021) 65.34 406.71 T
X(=) 67.59 406.71 T
X(1) 74.94 412.6 T
X(4) 74.94 400.52 T
X(1) 86.1 406.71 T
X3 F
X(c) 118.92 406.71 T
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  # end of 'lic.1.2/doc/siggraph93/paper.ps.B'
fi
if test -f 'lic.1.2/lic/Makefile.tmpl' -a "${1}" != "-c" ; then
  echo shar: Will not clobber existing file \"'lic.1.2/lic/Makefile.tmpl'\"
else
  echo shar: Extracting \"'lic.1.2/lic/Makefile.tmpl'\" \(1106 characters\)
  sed "s/^X//" >'lic.1.2/lic/Makefile.tmpl' <<'END_OF_FILE'
X#
X# $Header: /d/sisal/a/casey/tmp/lic/lic/RCS/Makefile.tmpl,v 1.1 1993/05/18 16:59:50 casey Exp $
X#
X      DEFINES = $(MMAP_DEFINES)
XSYS_LIBRARIES = -lm
X
X         SRCS = lic.c
X         OBJS = lic.o
X      PROGRAM = lic
X         MANS = lic.1
X
X          ALL = $(PROGRAM)
X
Xall: $(ALL)
X
Xincludes:
X
X$(PROGRAM): $(OBJS) $(LIBLIC)
X    $(CC) $(CFLAGS) -o $(PROGRAM) $(OBJS) $(LIBLIC) $(SYS_LIBRARIES)
X
Xinstall: $(PROGRAM) $(BINDIR) install_$(MANINSTALL)
X    rm -f $(BINDIR)/$(PROGRAM)
X    cp $(PROGRAM) $(BINDIR)/$(PROGRAM)
X    $(STRIP) $(BINDIR)/$(PROGRAM)
X    chmod $(INSTBINPROT) $(BINDIR)/$(PROGRAM)
X
Xinstall_man: $(MANROOT) $(MAN1DIR)
X    rm -f $(MAN1DIR)/lic.$(MAN1EXT)
X    cp lic.1 $(MAN1DIR)/lic.$(MAN1EXT)
X    chmod $(INSTMANPROT) $(MAN1DIR)/lic.$(MAN1EXT)
X
Xinstall_cat: $(MANROOT) $(MAN1DIR)
X    rm -f $(MAN1DIR)/lic.$(MAN1EXT)
X    $(NROFF) -man lic.1 > $(MAN1DIR)/lic.$(MAN1EXT)
X    chmod $(INSTMANPROT) $(MAN1DIR)/lic.$(MAN1EXT)
X
Xinstall_none:
X
X$(BINDIR) $(MANROOT) $(MAN1DIR):
X    mkdir $@
X
Xclean:
X    rm -f $(PROGRAM) $(OBJS)
X    rm -f *~ *.o core a.out MAKELOG
X
Xlint:
X    lint -x $(ALLDEFINES) $(SRCS)
X
Xdepend:
X
Xlic.o: lic.c $(BUILDINCTOP)/lic.h
END_OF_FILE
  if test 1106 -ne `wc -c <'lic.1.2/lic/Makefile.tmpl'`; then
    echo shar: \"'lic.1.2/lic/Makefile.tmpl'\" unpacked with wrong size!
  fi
  # end of 'lic.1.2/lic/Makefile.tmpl'
fi
echo shar: End of archive 3 \(of 10\).
cp /dev/null ark3isdone
MISSING=""
for I in 1 2 3 4 5 6 7 8 9 10 ; do
    if test ! -f ark${I}isdone ; then
    MISSING="${MISSING} ${I}"
    fi
done
if test "${MISSING}" = "" ; then
    echo You have unpacked all 10 archives.
    rm -f ark[1-9]isdone ark[1-9][0-9]isdone
else
    echo You still must unpack the following archives:
    echo "        " ${MISSING}
fi
exit 0
exit 0 # Just in case...