o54 2015011314 [email protected] 2017 c6 25 fzpzhou/data/ppm-report.pdf ·...

21
˜ uB Wzier ¡ n E . / O¯ª¢w O54 ² 2015011314 [email protected] 2017 c 6 25 F

Upload: others

Post on 15-Jul-2020

0 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

ÄÄÄuuuBWWWzier­­­¡¡¡���nnn���EEE...������///O�Åã/Æ— ¢��w

O54 ±�² 2015011314

[email protected]

2017c 6� 25F

Page 2: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

8¹ 1

888¹¹¹

1 ¢¢¢���SSSNNN.................................................................... 2

1.1 Ä�õU ........................................................................................ 2

1.2 N\õU ........................................................................................ 2

2 VVVnnngggBezier­­­¡¡¡EEE... ................................................ 3

2.1 Bezier­¡:�I ........................................................................... 3

2.2 Bezier­¡��þ!{�þ ............................................................ 4

2.3 Bezier­¡¦�............................................................................... 5

2.3.1 è�o©{+��Ý ................................................................................ 5

2.3.2 ÚîS�{ .............................................................................................. 7

2.4 Bezier­¡«n............................................................................... 8

3 |||µµµ���///....................................................................10

3.1 1�Jl�{ ................................................................................. 10

3.1.1 µ��{.................................................................................................. 12

3.1.2 �æ�|ç¸�{ ................................................................................... 13

3.2 ì?ª1fN��{£PPM¤ ...................................................... 14

3.2.1 PASS1—1�Jlïá-E:ã ............................................................. 15

3.2.2 PASS2—1fu� ................................................................................... 16

4 ���ªªª(((JJJ....................................................................17

4.1 �/�Jã..................................................................................... 17

4.2 Obj©��ã .................................................................................. 19

Page 3: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

1 ¢�SN 2

1 ¢¢¢���SSSNNN

1.1 ÄÄÄ���õõõUUU

�¢�¥§�¦ÄuBWzier­¡?1n�E.��/"

3/­¡E.0�!§·¢yVngBWzier­¡�¦�£(Üè�o©{9ÚîS�{¢

y¤§¿|^§�Eõ«�.§�)�¡!xò!u»�¶

ã 1: �¡ ã 2: u»

3/|µ�/0�!§·¢yÄuì?ª1fN�£PPM�{¤��Û1ì�.£ë�Ø

©Progressive Photon Mapping (Toshiya Hachisuka, et al.)¢y¤§�/�JØ=äk�p�°O

ݧ��±���{/NyCaustics�X�q���J"

ã 3: X�q��Caustics ã 4: «n[!

1.2 NNN\\\õõõUUU

3Ä�õU�§·�¢yAABB��ݦ�\�!«nbã£�)­¡«n!²¡«n!

Page 4: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

2 VngBEZIER­¡E. 3

¥¡«n¤!µ��J!�æ�|ç¸�ÿÐõU§{ãXeµ

• AABB��ݵ3è�o©{+ÚîS�{¢yVng­¡¦��L§¥§I�éo©��

�z��­¡����ݦ��䧿rk�:��­¡\è"ù��5§BçK­¡�

�Ü©Ã�:Ü©§��ü$O�¤�"du­¡õ��5�§�:ê8Øõ§�T�{

E,Ý=�O(log N) §\��JwÍ"

• «nbãµÒ¢yJÝ ó§²¡«n�¥¡«n�é�´§�I��{ü�IC�=�¶

, éuVngBezier­¡ ó§du·¦��æ^o©{§�e5�ÚîS�{=U�Ñ

�­¡�(u, v)�§ J±¼��­¡�(u, v)�I"�)ûù�´¶§·s¤���m?

1g�§¿�ª�M�«¢y{²�N\O�¤�4$��{§ò3�©�[0�"

• µ��Jµ�âµ�n��1�!�å!Ôå§é1��Ñu:31�þ���Å6ħ¿

(�1�EUà�u½Â��²¡þ"¢�¥§��Åæ�gê�10g§�±�Ð/²ï�

/�J��/�m"

• �æ�|縵T�{Ì��é1�Jl§duV\µ��J��§ç¸�B���z§

� 31fN�)¤�ã¡¥�æ^T�{"Ì�6§�µéz�ÔN§3�E�(½��

�Å�id�¶z����o��MF�§P¹����ôÚ�=ÔNk'"�r��§�I

ÄkçÀÑ@MF��þe�mØÓ���§�EI�r��>.¶ �é>.þ�z�

���©�4§éù4�f���u��^1�?1�æ�§¿é¼��4�ôÚ��²þ��

�>.����ªôÚ"

2 VVVnnngggBezier­­­¡¡¡EEE...

2.1 Bezier­­­¡¡¡:::���III

VngBezier­¡d16���:�¤§z�:��I�Ñ´��:3ËÏd"ļê�^e�

\�Ú"

P (u, v) =

3∑i=0

3∑j=0

B3i (u)B

3j (v)Pij

3§S¥§�â(u, v)�I(½Bezier­¡þ��´�þ�9�ö���"3ë��

ä] £https://www.scratchapixel.com/lessons/advanced-rendering/bezier-curve-rendering-utah-

teapot¤¥�¢y��§�ª¢y��I�{�µÄk�½u§(½v��þ�4���:§(½�

^÷Xv��òÐ�Bezier­�¶,�3ù^v���Bezier­�þ§�âv�¦Ñ�ª��I�"

3Bezier­�þ§¦Ñëê�t��:��I�§�è¢yXãµ

3Bezier­¡þ§¦Ñëê�(u, v)��:��I�§�è¢yXãµ

Page 5: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

2 VngBEZIER­¡E. 4

ã 5: Bezier­¡�I

ã 6: Bezier­�:�I�{

ã 7: Bezier­¡:�I�{

2.2 Bezier­­­¡¡¡������þþþ!!!{{{���þþþ

3�©AÛ¥§­¡���þ�±^­¡� �ê5L«"AO/§éBezier­¡�I�§

¦�ê�§Ó�Äk�½���ݧ¼��^÷XU½öV��òÐ�­�¶ �éù^­�¦�

ê"

Bezier­���þ�O��{Xeãµ

Bezier­¡��þ�O��{Xeã£ã¥�V��� �ê§U����aq¤µ

kUÚV��� �ê§B�±ÏLò �ê?1�¦§¼�T:?�{�þµN = U × V§

ù31�Jl�{¥åX­���^"

Page 6: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

2 VngBEZIER­¡E. 5

ã 8: Bezier­���þ�{

ã 9: Bezier­¡��þ�{

2.3 Bezier­­­¡¡¡¦¦¦���

Bezier­¡�¦��{§´�g§S?�¥���J:"²L�ÓÆ�?Ø!�þ�á�Â8

ó���§�n�������p��­½��{6§µ

• è�o©µïá��è�§zgòèÄ­¡o©§òf­¡¥���Ýk��@\\è�§

��è��½ö�{­¡v���¶

• ÚîS�µéè�¥�{�v��­¡$1ÚîS�{§ÀJÙ¥��ål�Cö§�Ù

{�þ!�:�I!«nôÚ�£þ�N^"

2.3.1 è�o©{+��Ý

|^Bezier­¡�à�5§3òf­¡o©?n��§��1����ÝÃ�:§=�òTf

­¡�±�ï"

§S¥¢yAABB��ݧë�O�Åã/Æ��¥�Slab¯�¦��{9Ü©�ä] ¢

y£!À¤µ

�±��§du�ÜBezier­¡é�§XJ��3þ¡$1ÚîS�{§KéN´��$�!

ê�Ø­½�(J" o©{¥§æ��´aqul�ä��{�\�g�§òÚîS�{�©:

Û�u�����S§��¡§��Jp�Ç£éêE,ݤ¶,��¡§¦�ÚîS�{k�

���Ün�Щ�§´�«ê�­½�)û�Y"

Page 7: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

2 VngBEZIER­¡E. 6

ã 10: AABB��ݦ��{

¢Sö�¥§�ò­¡�©�4§ØU{ü/æ��©�{§ÄK#�­¡3©�?òØU²

wq�"�«�Ð�¢y�{��þQ²0�L�De Casteljau�{§=é��:?1�5��§

±�y��²wµ��­¡���:�P[]§LÚR©O´�­¡©�Ñ5�#­¡§K��¦^±

eúªµ

L0 = P0

L1 = P0/2 + P1/2

L2 = P0/4 + P1/2 + P2/4

L3 = P0/8 + 3P1/8 + 3P2/8 + P3/8

,��f­¡R�úª�L��é¡"ù�úªò��d�)ö3¢y«nbã�êÆí��

Ä:§u�­���^"�è¢yXãµ

Page 8: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

2 VngBEZIER­¡E. 7

ã 11: De Casteljau��o©�{

2.3.2 ÚîS�{

3ÏLo©{§¼�¤k�U�k�:��­¡��§é­¡$1ÚîS�{§|^ê�)

{¦Ñ�:§¿3¤k�:¥§¼�ål�����"

ÚîS�{÷vS�úªµxn+1 = xn − J−1F (xn)§Ù¥J�éA�JacobiÝ"¢�¥§�

S�gê�50g§éA�è¢yXeµ

ã 12: ÚîS�{

Page 9: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

2 VngBEZIER­¡E. 8

2.4 Bezier­­­¡¡¡«««nnn

3±þÄ��{®²¢y��§)ö������(JB´�Bezier­¡V\«n"c¡®²

Qã§du)ö3¦��§æ^è�o©{?1\�§ù���âf­¡�(u, v)�I�í�­

¡�(u, v)�IC�É~qJ", §)ö3éþ¡���o©{?1�\�ïÄ��§�gÑ

�«N\¤�4$��{£�,§)öíÿ§c¡���o©�{B´Äuù�5ÆJÑ�§ù«

�{�½Q��c�ÆöMEÑ5§�)ö3¢�¥(¢´ÄuÕá�í�¤§{ãÙ�nXeµ

Äk§òþ¡���o©{�¤Ý/ª§�±��µ

·�Ø�òþªP�L = AP�/ª"2(ÜBezier­�:�I�O�úªµ

2òþªP�f(t) = BP�/ª"� §(ܱþ2ª§�±�ѵ

f(t) = (BA−1)L

¦�A�_Ý�µ

�\f(t) = (BA−1)L¥O�§�±uy§·^uP�ëêt§Tд·^uf­¡L�ëê2t"

�d§)öîú¸,mKµ���/Xd§@o���/§Ø�T�ÌÓ��êÆ�{íºf

­¡�(u, v)§A���­¡Ó�/÷v2��êþ'X"AO/§�±�ÑXeßÿµ£±e`²

¥§uP , vP��­¡��I§uL, vL�f­¡��I¤

Page 10: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

2 VngBEZIER­¡E. 9

�d§�����Äu­¡o©{�«n�{¥y3)ö¡cµ3è��z�!:Nodea¥§

O\�;4�ëêµkU, bU, kV, bV§^u|^f!:�UV��íI!:�UV�"lI!:�f!

:§�âþã�5ƧØä�#ù4�Xê§=����­¡¥�UV�Iµ

uorigin = kU ∗ ufinal + bU

vorigin = kV ∗ vfinal + bU

�è¢yXãµ

²L?§¢y§)ö(@ù«�{��(5§¿¼����{%ý�­¡«nbã�Jµ

Page 11: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

3 |µ�/ 10

ã 13: ­¡«nbã�J

�¡Úò¶éA�Obj©�Xeµ

ã 14: �¡Obj ã 15: ò¶Obj

3 |||µµµ���///

3.1 111���JJJlll���{{{

1�Jl£Ray Tracing¤´�«k���/�{§Ù�n´Ä��Ôn5Ƶ��¦�¶4

þ��P�ôÚ§·��IlÀ:uÑ�^²LP�1�§é��|µ¥ÔN�1���:Q"�

:Q�ôÚ�Ò´��P�ôÚ¶·��I¦ÑÔNþQ:�ôÚ§B�Ò¦���P�ôÚ"

Page 12: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

3 |µ�/ 11

ã 16: 1�Jl�nã

ã 17: ��1ì�m�1ì

1�Jl���èXeµ

Ù¥§û��¦^Phong�.O�µ

Page 13: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

3 |µ�/ 12

3.1.1 µ��{

3þ¡�Ú½¥§1�ÚI�l�ÅuÑ�^��|µ�1�"µ��{§K´ÏL31�

þ§é1��å:?1�Åæ�§Ó��y1���:Eò®àu�½��²¡"

Ø%�è¢yXeµ

3¢�¥§)ö��Åæ�gê�50§�/Ñ��JXãµ

Page 14: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

3 |µ�/ 13

ã 18: µ��J

3.1.2 �æ�|ç¸�{

31�Jl�/Ñ�ã¡¥§��éî­�¯KB´ç¸y�î­"

�«1�k���ÇØ���{§��æ�|ç¸�{"äN¢y�{�µéz�ÔN§3�

E�(½���Å�id�¶z����o��MF�§P¹����ôÚ�=ÔNk'"�r�

�§�IÄkçÀÑ@MF��þe�mØÓ���§�EI�r��>.¶ �é>.þ�z

����©�4§éù4�f���u��^1�?1�æ�§¿é¼��4�ôÚ��²þ���

>.����ªôÚ"

)ö����JXeµ

ã 19: ²L�r��ÔNÚÒK>. ã 20: �²�r��ÔNÚÒK>.

Page 15: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

3 |µ�/ 14

�è¢yXeµ£du)ö�¢yPPM�{§é�k�1�Jl�è?1­�§ù�

����è¿��code�ÓJ�"XJsI�u�ùÜ©�è§�ue�w�·§·�e�

´[email protected]§·�±�suxù�����è¤

3.2 ììì???ªªª111fffNNN������{{{£££PPM¤¤¤

)ö3@ýïÖØ©Progressive Photon Mapping (Toshiya Hachisuka, et al.)§¿(

ÜRealistic Image Synthesis using Photon Mapping (Henrik Wann Jenson)�Ö?19Ïn)�

�§ªuqJ/n)PPM�{�Ä��n"ÙÄ�6§Xeµ

• 1�Jl£PASS1¤µÄk§�âþ�!�ã�1�Jl�{§é|µ¥�z���?11

�Jl§(½�z���P�'é�-E:hp1, hp2, ...£Ï�1�Jl�k3-�û��L¡

â¬Ê�48§� ·�w��-E:ôÚÙ¢Ñ��½öm�/5gu,�û��L¡¤"

äNö��§éz�û��L¡�;Ù'é�-E:§z�-E:�X1��D4§Ù�

�weight�A/U\÷åÔN�ôÚ¶

• 1fu�£PASS2¤µ3ÏLPASS1ïá��|µ�-E:ã��§lz�1 u��½

êþ�1f�|µ¥§z�1f�3û��L¡§Ò3-E:ã£KDTree¤¥Î¯µ/ù�

1f3=-E:��»Sܺ0òù�1f���1Ïþ\O��Î�£�-E:¥§¿O

\z�-E:�#O1fOêì¶

• �#-E:ã&Eµ©�2�Ü©µÄk§z�-E:�\O1ÏþÚ�»I��#¶Ùg§

-E:ã¥�z�:�o����»I��#"�#�§�âØ©¥�±eúª§?1¢y

Page 16: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

3 |µ�/ 15

£N��©\O1fê§M��Ó#O1fê§R2��-E:�»§φP�\O1Ïþ§α��

�P~�Çk�~ꤵ

k =N + αM

N +M;

R2∗ = k;φP ∗ = k;

N+ =M ;M = 0;

• �O�Ý�µ�âz���éA�-E:§9�-E:�\O1fê§�±�Ñ�ª¶4þ

,����(x, y)�ôÚ��O��£Ù¥§ã���ÝI�ÏLëêλ?1N!§¢�¥u

yéuº�ØÓ�|µ!ØÓ�1fê§TëêI�ØÓ��¤

photo[x][y] = λ∑ hp.φP

hp.R2 ·Nemit

±e§ÒPASS1ÚPASS2üÚ?1�ã"

3.2.1 PASS1—1�Jlïá-E:ã

�âØ©¥�£ã§z�-E:�;Xe&Eµ

é|µ¥¤k�û��ÔN§�;-E:¶-E:�ôÚ´÷å²L�¤kÔN�ôÚU\"

�è¢yXeµ

Page 17: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

3 |µ�/ 16

-E:ãæ^KDä?1¢y§�±�¯/¢y���ÎõUµ

3.2.2 PASS2—1fu�

ùp§z�1 §�âÙUþ©Ù§�|µ¥�Å/u�1f£)öæ^OpenMP`z5

U§�uycstdlib¥��Åêrand()¼ê�§ØS�§I�zg­#srand¤§�è¢yXeµ

ù�Ú¥§�±uy§ëêα�����§�»Âñ��¯§�(J��Ø°[¶ëêЩ�

»INIT RADIUS�����§|µ¥�pªD(�زw§���E¤�¯K´§d�éu�

¿S|µ£XxG�ݤp��ÒK¬'�î­µ

Page 18: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

4 �ª(J 17

ã 21: ���Щ�»§p�k�î­�ÒK ã 22: ���Щ�»§pªD(î­

4 ���ªªª(((JJJ

4.1 ���///���JJJããã

ã 23: <Ù6c£1fN�¤

Page 19: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

4 �ª(J 18

ã 24: <Ù6c2£1fN�¤

Page 20: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

4 �ª(J 19

ã 25: <Ù6c£1�Jl¤

4.2 Obj©©©������ããã

ã 26: ò¶

Page 21: O54 2015011314 zhouzp15@mails.tsinghua.edu.cn 2017 c6 25 Fzpzhou/data/ppm-report.pdf · ˜˜˜uuuB›››¡¡¡˙˙˙ nnn‚‚‚EEE...ƒƒƒ /// O”¯ª/˘| ¢ w O54 – †2015011314

4 �ª(J 20

ã 27: �¡

ã 28: u»