-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathdissections_project_page.html
More file actions
218 lines (124 loc) · 8 KB
/
dissections_project_page.html
File metadata and controls
218 lines (124 loc) · 8 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<!-- saved from url=(0061)http://people.sutd.edu.sg/~saikit/projects/fashion/index.html -->
<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Zoomorphic Design</title>
<meta http-equiv="Content-Language" content="en-us">
<meta content="MSHTML 6.00.6000.16674" name="GENERATOR">
<style type="text/css">
<!--
.style1 {
font-family: "Times New Roman", Times, serif;
font-weight: bold;
}
.style2 {font-family: "Times New Roman", Times, serif}
.style7 {font-size: 16px}
-->
</style>
<script type="text/javascript" async="" src="./index_files/ga.js"></script><script type="text/javascript">
var _gaq = _gaq || [];
_gaq.push(['_setAccount', 'UA-22603262-4']);
_gaq.push(['_trackPageview']);
(function() {
var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
})();
</script>
</head>
<body style="TEXT-ALIGN: center" class=" hasGoogleVoiceExt"><div id="StayFocusd-infobar" style="display:none;">
<img src="chrome-extension://laankejkbhbdhmipfmgcngdelahlfoji/common/img/eye_19x19_red.png">
<span id="StayFocusd-infobar-msg"></span>
<span id="StayFocusd-infobar-links">
<a id="StayFocusd-infobar-never-show">hide forever</a> |
<a id="StayFocusd-infobar-hide">hide once</a>
</span>
</div>
<p align="center"><b><font face="Times New Roman" size="6">Approximate Dissections</font></b></p>
<div align="center">
<table width="1000" border="0" id="table1">
<tbody>
<tr>
<td><p align="center"><b><font face="Times New Roman" size="5">Noah Duncan<sup>1</sup></font></b></p></td>
<td><p align="center"><b><font face="Times New Roman" size="5">Lap-Fai Yu<sup>2</sup></font></b></p></td>
<td><p align="center"><b><font face="Times New Roman" size="5">Sai-Kit Yeung<sup>3</sup></font></b></p></td>
<td><p align="center"><b><font face="Times New Roman" size="5">Demetri Terzopoulos<sup>1</sup></font></b></p></td>
</tr>
</tbody></table>
<table width="1000" border="0" id="table1">
<tbody>
<tr>
<td><p align="center"><b><font face="Times New Roman" size="4"><sup>1</sup>University of California, Los Angeles</font></b></p></td>
<td><p align="center"><b><font face="Times New Roman" size="4"><sup>2</sup>University of Massachusetts Boston</font></b></p></td>
<td><p align="center"><b><font face="Times New Roman" size="4"><sup>3</sup>Singapore University of Technology and Design</font></b></p></td>
</tr>
</tbody>
</table>
<!--<p><img src="images/teaser.jpg" alt="" width="1100" /></p>-->
<!--p><img src="./index_files/flowchart4.png" alt="" width="1000"></p-->
<br>
<br>
<table width="1000" border="0">
<tbody><tr>
<td><div align="center"><img src="img/dissection_teaser_0.png" alt="" width="500"></div></td>
<td><div align="center" width="200"></div></td>
<td><div align="center"><img src="img/dissection_teaser_1.png" alt="" width="500"></div></td>
</tr>
<tr>
<td><div align="center"><em>Input Shapes</em></div></td>
<td><div align="center" width="200"></div></td>
<td><div align="center"><em>Output Dissection</em></div></td>
</tr>
</tbody></table>
<p align="left"><span class="style2"><b><font size="5">Abstract</font></b>
A geometric dissection is a set of pieces which can be assembled in different ways to form distinct shapes. Dissections are used as recreational puzzles because it is striking when a single set of pieces can construct highly different forms. Existing techniques for creating dissections find pieces that reconstruct two input shapes exactly. Unfortunately, these methods only support simple, abstract shapes because an excessive number of pieces may be needed to reconstruct more complex, naturalistic shapes. We introduce a dissection design technique which supports such shapes by only requiring that the pieces reconstruct the shapes approximately. We find that in most cases, a small number of pieces suffices to tightly approximate the input shapes. We frame the search for a viable dissection as a combinatorial optimization problem, where the goal is to search for the best approximation to the input shapes using a given number of pieces. We find a lower bound on the tightness of the approximation for a partial dissection solution, which allows us to prune the search space and makes the problem tractable. We demonstrate our approach on several challenging examples, showing that it can create dissections between shapes of greater complexity than those supported by previous techniques.
</span></p>
<p align="left" class="style2"><span class="style7"><strong>Keywords</strong>: : computational geometry, dissection</span></p>
<h2 align="left"><font face="Times New Roman">Publications:</font></h2>
<ul>
<li>
<p align="left"><strong><font face="Times New Roman">Approximate Dissections</font></strong><font face="Times New Roman"><br>
<a href="index.html">Noah Duncan</a>,
<a href="https://www.cs.umb.edu/~craigyu/">Lap-Fai Yu</a>,
<a href="http://people.sutd.edu.sg/~saikit/">Sai-Kit Yeung</a>
<a href="http://web.cs.ucla.edu/~dt/">Demetri Terzopoulos</a>
<br> ACM Transactions on Graphics (Proceeding of <b>SIGGRAPH ASIA 2017</b>)
<br><a href="http://web.cs.ucla.edu/~nduncan/pdf/dt-final-paper-dissections.pdf">Paper</a><span class="bodyText STYLE3">, <a href="https://www.youtube.com/watch?v=fe__w-05yVc">Video</a>
<br>
<br>
<!--
</span></font></p><h3 align="left"><font face="Times New Roman"><b><font face="Times New Roman">BibTex:</font></b></font></h3><font face="Times New Roman">
<p align="left"><font face="Times New Roman">@article{zoomorphic,<br>
</font><font face="Times New Roman" color="#000000">
author </font><font face="Times New Roman">= {Noah Duncan and Lap-Fai Yu and Sai-Kit Yeung and Demetri Terzopoulos},<br>
</font><font face="Times New Roman" color="#000000">title </font><font face="Times New Roman">=
{<font color="#000000">Approximate Dissections</font>},
<br>
booktitle = {</font><span lang="EN-US" style="FONT-FAMILY: "Times New Roman"">ACM Trans. Graph.</span><font face="Times New Roman">},<br>
volume = {34}<br>
pages = {95:1--95:13}<br>
number = {4}<br>
year = {2015}<br>
}</font></p>
-->
<p align="left">
<iframe width="630" height="472" src="https://www.youtube.com/embed/fe__w-05yVc" frameborder="0" allowfullscreen></iframe>
</p>
</font></li></ul><font face="Times New Roman">
<h3 align="left">Acknowledgements:</h3>
<p align="left">
We thank Michael S. Brown for narrating the video and Quang Trung Truong for assistance in fabricating the results. Yu was supported in part by National Science Foundation award number 1565978 and by the Joseph P. Healey Research Grant Program provided by the Office of the Vice Provost for Research and Strategic Initiatives and by the Dean of Graduate Studies of UMass Boston. Yeung was supported in part by Singapore MOE Academic Research Fund MOE2016-T2-2-154 and by a grant from the National Heritage Board of Singapore. Duncan was supported in part by the SUTD Digital Manufacturing and Design (DManD) Centre, which is supported by the National Research Foundation (NRF) of Singapore. This research was also supported by the NRF under its IDM Futures Funding Initiative and Virtual Singapore Award No. NRF2015VSG-AA3DCM001-014. We are grateful to the anonymous reviewers for their constructive comments
</p>
<hr align="center" width="100%" size="2">
<h2 align="left" class="style2">Results:</h2>
<table align="center" width="1000" border="0">
<tbody>
<tr><th><img src="img/dissection_results.png" alt=""></th></tr>
</tbody>
</table>
<br>
<br>
<p align="left">
</p><p align="left">
</p><p></p>
</font></div><font face="Times New Roman">
</font></body></html>