powerpoint - 3dscenecgg.mff.cuni.cz/~pepca/lectures/pdf/3dscene.pdf · 2001. 10. 12. ·...

27
5HSUH]HQWDFH’VFkQ\ {-RVHI3HOLNgQ .69,0))8.3UDKD HPDLO-RVHI3HOLNDQ#PIIFXQLF] :::KWWSFJJPVPIIFXQLF]aSHSFD

Upload: others

Post on 07-Feb-2021

2 views

Category:

Documents


0 download

TRANSCRIPT

  • 5HSUH]HQWDFH��'�VFkQ\

    {�����������-RVHI�3HOLNgQ

    .69,�0))�8.�3UDKD

    H�PDLO��-RVHI�3HOLNDQ#PII�FXQL�F]

    :::��KWWS���FJJ�PV�PII�FXQL�F]�aSHSFD�

  • 0HWRG\�UHSUH]HQWDFH��'�VFkQ

    X �REMHPRYk�UHSUH]HQWDFH SÎmPk�LQIRUPDFH�R�YQLWÎQmFK�REMHPHFK�WÀOHV

    VQDGQ¬�WHVW�ERGWÀOHVR��OH©m�GDQ¬�ERG�XYQLWÎWÀOHVD"���]REUD]RYgQm�PÖ©H�E¬W�REWm©QÀM§m

    SRX©mYDMm�VH�Wk©�MDNR�SRPRFQk�GDWRYk�VWUXNWXU\SUR�U\FKOk�Y\KOHGgYgQm

    X �SRYUFKRYk�UHSUH]HQWDFH SÎmPk�LQIRUPDFH�R�SRYUFKX�WÀOHV��KUDQ\��VWÀQ\�

    REWm©QÀM§m�WHVW�ERGWÀOHVR��WÀOHVD�YÖEHF�QHPXVmPmW�YQLWÎQm�REMHP���SRPÀUQÀ�VQDGQk�]REUD]RYgQm

  • 2EMHPRYk�UHSUH]HQWDFH

    ��Y¬³WRYk�UHSUH]HQWDFH SÎmPk�Y\³mVOHQm�REVD]HQkKR�SURVWRUX��GLVNUkWQm

    UHSUH]HQWDFH���RPH]HQg�SÎHVQRVW�

    SRX©mYDMm�VH�KODYQÀ�MDNR�SRPRFQk�GDWRYk�VWUXNWXU\

    SUR�U\FKOk�Y\KOHGgYgQm

    EXQÀ³Q¬�PRGHO��RNWDQWRY¬�VWURP

    ��&6*�UHSUH]HQWDFH YHOLFH�VLOQg�D�SÎHVQg�PHWRGD��HOHPHQWgUQm�WÀOHVD�

    JHRPHWULFNk�WUDQVIRUPDFH��PQR©LQRYk�RSHUDFH�

    REWm©QÀM§m�]REUD]RYgQm��YUKgQm�SDSUVNX�

  • %XQÀ³Q¬�PRGHO

    YR[HO

    SROH�N®O®P�YR[HO×MHGQRELWRYg�YDULDQWD������QLF������WÀOHVRYmFHELWRYg�YDULDQWD������QLF��Q�!�����WÀOHVR�³mVOR�Q

    YROXPH��HOHPHQW

  • =REUD]RYgQm�EXQÀ³QkKR�PRGHOX

    ·�NUHVOHQm�RG]DGX�GRSÎHGX SRX]H�SÎLYUgFHQk�VWÀQ\�YR[HOÖ

    SRX]H�VWÀQ\�QD�SRYUFKX�WÀOHV��VWÀQ\�PH]L���D�!��

    YmFHQgVREQk�SÎHNUHVORYgQm

    ·�VSHFLgOQm�SURPmWgQm YHOPL�HIHNWLYQm�DOJRULWPXV�EH]�]E\WH³QkKR

    SÎHNUHVORYgQm

    $QW�DWWDFN�QD�=;�6SHFWUX����������YR[HO�

  • 6SHFLgOQm�SURPmWgQm

    [[

    ���KRUQm�VWÁQD>�����@

    ���SUDYg�VWÁQD>�����@

  • 6SHFLgOQm�SURPmWgQm

    ���OHYg�VWÁQD>�����@

    ���KRUQm�VWÁQD>�����@

    [ [

  • 2NWDQWRY¬�VWURP��RFWUHH�

  • 2NWDQWRY¬�VWURP

    X ��'�DQDORJLH�NYDGUDQWRYkKR�VWURPX MH�OL�YQLWÎHN�NU\FKOH�QHKRPRJHQQm��UR]GÀOm�VH�QD

    RVP�³gVWm��GÀOm�VH�D©�GR�rURYQÀ�YR[HOX�

    rVSRUD�SDPÀWL�SURWL�EXQÀ³QkPX�PRGHOX

    ·�NUHVOHQm�RG]DGX�GRSÎHGX SRX]H�SÎLYUgFHQk�VWÀQ\�NU\FKOm

    SRX]H�VWÀQ\�QD�SRYUFKX�WÀOHV��VWÀQ\�PH]L���D�!��

    QÀNROLNDQgVREQk�SÎHNUHVORYgQm�QÀNWHU¬FK�SL[HOÖ

  • .UHVOHQm�RG]DGX�GRSÎHGX

    � �

    � � �

    � �

    ��SRÏDGm�

    ���������������

    ��SRÏDGm�

    ���������������

  • &6*��&RQVWUXFWLYH�6ROLG�*HRPHWU\�

    X �HOHPHQWgUQm�JHRPHWULFNg�WÀOHVD VQDGQR�GHILQRYDWHOQg�D�Y\³mVOLWHOQg

    NYgGU��SRORSURVWRU��KUDQRO��NRXOH��YgOHF��NX©HO����

    X �PQR©LQRYk�RSHUDFH NRPSR]LFH�VOR©LWÀM§mFK�WÀOHV�]�HOHPHQWgUQmFK

    VMHGQRFHQm��SUÖQLN��UR]GmO����

    X �JHRPHWULFNk�WUDQVIRUPDFH PRGLILNDFH�HOHPHQWgUQmFK�L�VOR©LWÀM§mFK�WÀOHV

    �KRPRJHQQm��PDWLFRYk�WUDQVIRUPDFH

  • &6*�VWURP

    7� 7�

    7� 7�

    T3· T1 T4· T1

    PQR©LQRYkRSHUDFH

    YVOHGHN

    HOHPHQWgUQmWÁOHVD

    JHRPHWULFNk�WUDQVIRUPDFH

  • 7UDQVIRUPDFH�Y�&6*�VWURPX

    X �Y¬]QDP��VkPDQWLND��WUDQVIRUPDFH�7L 7L�PRKRX�E¬W�XOR©HQ\�Y�ND©Gk�KUDQÀ�&6*�VWURPX

    SÎHYRG�VRXÎDGQLF�]H�VRXVWDY\�SRGWÀOHVD��SRGVWURPX�

    HOHPHQWgUQmKR�WÀOHVD��GR�VRXVWDY\�QDGWÀOHVD

    SRGWÀOHVR�WUDQVIRUPXML�SRPRFm�7L�SÎHG�WmP��QH©�KRSÎLGgP�GR�QDGWÀOHVD

    ·�VQDGQg�WUDQVIRUPDFH�OLERYROQkKR�SRGVWURPX ]PÀQmP�SRX]H�MHGQX�PDWLFL

    ·�LQYHU]Qm�WUDQVIRUPDFH�7L��

    SUR�Y\³mVORYDFm�DOJRULWP\��WHVW�ERG&6*��]REUD]HQm�

  • 7UDQVIRUPDFH�Y�&6*�VWURPX

    ·�XOR©HQm�WUDQVIRUPDFm�MHQ�Y�OLVWHFK NXPXORYDQk�VRX³LQ\��QDSÎ��T3· T2· T1 QHERLQYHU]Qm�T1

    -1· T2-1· T3

    -1�

    XU\FKOHQm�Y\³mVORYDFmFK�DOJRULWPÖ��SUR�HGLWDFL�MH

    Y¬KRGQÀM§m�GLVWULEXRYDQk�XOR©HQm�WUDQVIRUPDFm�

    ·�rVSRUQk�XOR©HQm�HOHPHQWgUQmFK�WÀOHV WÀOHVD�MVRX�XOR©HQD�Y�QRUPRYDQkP�WYDUX��Y§HFKQ\]PÀQ\�VH�SURYgGm�JHRPHWULFN¬PL�WUDQVIRUPDFHPL

    NU\FKOH��MHGQRWNRYg��YUFKRO�Y�SR³gWNX���NRXOH

    �MHGQRWNRYg��VWÎHG�Y�SR³gWNX���YgOHF��YRGRURYQg

    SRGVWDYD���MHGQRWNRY¬�NUXK��VYLVOg�RVD��Y¬§ND��������

  • 7HVW�ERG&6*�VWURP

    X �OH©m�GDQ¬�ERG�$�XYQLWÎ�WÀOHVD" QÀNG\�FKFHPH�]MLVWLW�L�SRGWÀOHVD�REVDKXMmFm�ERG�$

    ·�WHVW\�ERGHOHPHQWgUQm�WÀOHVR�MVRX�VQDGQk��SÎHGHY§mP�SUR�QRUPRYDQk�WYDU\�WÀOHV�

    ·�SUÖFKRG�&6*�VWURPHP VRXÎDGQLFH�ERGX�$�VH�SÎHYgGÀMm�GR�VRXÎDGQ¬FKVRXVWDY�HOHPHQWgUQmFK�WÀOHV��LQYHU]Qm�WUDQVIRUPDFH�

    PmVWR�PQR©LQRY¬FK�RSHUDFm�VH�SURYgGÀMm�MHMLFK

    ERROHRYVNk�HNYLYDOHQW\��∨�PmVWR�∪��∧�PmVWR�∩������

  • 7HVW�ERG&6*�VWURP

    7� 7�

    7� 7�

    bod A· T1-1· T3

    -1

    ERG�$

    bod A· T1-1

    bod A· T1-1· T4

    -1

    bod A· T2-1

    8YQLWÏ 0LPR

    0LPR

    8YQLWÏ

  • =REUD]RYgQm�&6*�UHSUH]HQWDFH

    ·�SÎHYHGHQm�GR�SRYUFKRYk�UHSUH]HQWDFH SUR�ND©G¬�GUXK�HOHPHQWgUQmKR�WÀOHVD��UXWLQDSÎHYgGÀMmFm�WÀOHVR�QD�PQRKRVWÀQ

    PQR©LQRYk�RSHUDFH�QDG�PQRKRVWÀQ\��RPH]HQgSÎHVQRVW���Y¬VOHGHN�QHPXVm�E¬W�VSUgYQÀ�DQL�Y

    WRSRORJLFNkP�VP\VOX�

    ·�YUKgQm�SDSUVNX��5D\�FDVWLQJ� SÎHVQk�]REUD]RYgQm�Y�UDVWURYkP�SURVWÎHGm�SL[HORYg�SÎHVQRVW�

    Y¬SR³HWQÀ�QgUR³QÀM§m�PHWRGD

  • 3RYUFKRYk�UHSUH]HQWDFH

    ��GUgWRY¬�PRGHO SVHXGR�SRYUFKRYg�UHSUH]HQWDFH

    SRX]H�YUFKRO\�D�KUDQ\�WÀOHV��QHO]H�SRX©mW�SURY¬SR³HW�YLGLWHOQRVWL�

    ��9+6�7��UHSUH]HQWDFH NRPSOHWQm�WRSRORJLFNg�LQIRUPDFH��VH]QDP\�YUFKROÖ�KUDQ��VWÀQ��D�WÀOHV�

    ��RNÎmGOHQg�KUDQD��ZLQJHG�HGJH� UHGXQGDQWQm�LQIRUPDFH�SUR�U\FKOk�Y\KOHGgYgQmVRXVHGQmFK�REMHNWÖ��KUDQ\�LQFLGHQWQm�V�YUFKROHP�����

  • 3RYUFKRYg�UHSUH]HQWDFH�9+67

    9�

    9�

    9�

    9�

    9�

    +�

    +�

    +�

    +�

    +�

    6�

    6�

    ���

    WÁOHVR�7�

    [

    \

    ]

    [

    \

    ]

    [

    \

    ]

    [

    \

    ]

    [

    \

    ]

    ���

    ���

    ���

    ���

    ���

    7����

    ���

    VWÁQ\

    WÁOHVD

    KUDQ\

    YUFKRO\

    6� 6�

    +� +� +� +� +�

    9� 9� 9� 9� 9�

  • 'ÀUDYg�VWÀQD

    XPÁOg�KUDQD�QHY\NUHVOXMH�VH�

  • ��PDQLIROG��PDQLIROG�

    'HI���3UR�ND©G¬�SRYUFKRY¬�ERG�H[LVWXMH�RNROm���NWHUk�MH�WRSRORJLFN\�HNYLYDOHQWQm�V�URYLQRX

    $QR

    1H

  • 2NÎmGOHQg�KUDQD��ZLQJHG�HGJH�

    ...

    VWÁQ\

    WÁOHVD

    KUDQ\

    [

    \

    ]

    [

    \

    ]

    YUFKRO\...

    [

    \

    ]

    ...

    ...

    ...WÁOHVR�7�

    9�9�

    9� 9�9�

    +� +�

    +�

    +� +�

    6� 6�

    +�

    9� 9� 9�

    7�

    6� 6�

    � �

    9� 9�

    6� 6�

    +� +�

    +� +�

  • 'DO§m�LQIRUPDFH�Y�GDWDEg]L

    X �YUFKRO� �QRUPgORY¬�YHNWRU�SUR�VSRMLWk�VWmQRYgQm�

    X �KUDQD� SÎm]QDN�XPÀOk�KUDQ\��SUR�UHSUH]HQWDFL�GÀUDY¬FK�VWÀQ

    QHER�DSUR[LPDFL�NÎLY¬FK�SORFK�VmWm�SRO\JRQÖ

    X �VWÀQD� EDUYD

    QRUPgORY¬�YHNWRU��VWmQRYgQm��SÎLYUgFHQg�RGYUgFHQg�

    X �WÀOHVR� EDUYD

  • (XOHURY\�]gNRQ\

    ·�SUR�MHGQRGXFK¬�SRO\HGU��EH]�GÀU��SODWm�Y]RUHF

    9���+���6� ��

    9���SR³HW�YUFKROÖ��+���SR³HW�KUDQ��6���SR³HW�VWÀQ

    ·�]REHFQÀQ¬�Y]RUHF��GRYROXMH�GmU\��

    V - H + S - D = 2· (T - G)

    '���SR³HW�GÀU�YH�VWÀQgFK��7���SR³HW�WÀOHV��*���SR³HWGÀU�SURFKg]HMmFmFK�FHO¬P�WÀOHVHP��*HQXV�

  • (XOHURY\�RSHUgWRU\

    ·�NRQVWUXNFH���PDQLIROGX�SR�NURFmFK Y�ND©GkP�NURNX�MH�]DML§WÀQD�SODWQRVW�(XOHURY¬FK

    Y]RUFÖ��WÀOHVR�MH�WRSRORJLFN\�NRUHNWQm�

    NH�ND©GkPX�RSHUgWRUX�H[LVWXMH�LQYHU]Qm��VQDGQg

    LPSOHPHQWDFH�SÎmND]X�XQGR�

    ·�SÎmNODG\�(XOHURY¬FK�RSHUgWRUÖ�0VIHYY�3��3����PDNH�VROLG��IDFH��HGJH��YHUWH[��YHUW��

    0HY�I��Y��3����PDNH�HGJH��YHUWH[�

    0HI�I��Y��Y����PDNH�HGJH��IDFH�

    .HI�H���NLOO�HGJH��IDFH�����

  • .RQVWUXNFH�³W\ÎVWÀQX

    ���0VIHYY�3��3�� ���0HY�I��Y��3��

    Y��3��Y��3��

    Y�

    Y��3��

    Y�H�

    H�I�

    V� V�

    I�H�

    ���0HI�I��Y��Y��

    Y�

    Y�

    Y�

    H�V�

    I�H�

    I�

    H�

    ���0HY�I��Y��3��

    Y�

    Y�

    Y�

    H�V�

    I�H�

    I�

    H�

    H�

    Y��3��

    ���0HI�I��Y��Y��

    Y�

    Y�

    Y�

    H�V�

    I�H�

    I�

    H�

    H�

    Y�

    H�

    I�

    ���0HI�I��Y��Y��

    Y�

    Y�

    Y�

    V�

    H�

    H�

    H�

    Y�

    H�

    I�I�

  • .RQHF

    'DO§m�LQIRUPDFH�

    Q -��)ROH\��$��YDQ�'DP��6��)HLQHU��-��+XJKHV�&RPSXWHU�*UDSKLFV��3ULQFLSOHV�DQG�3UDFWLFH�

    ����������������

    Q -LÎm�¨gUD�D�NRO���3R³mWD³RYg�JUDILND��SULQFLS\D�DOJRULWP\���������

    ·/$1�QD�0DOk�6WUDQÀ�

    EDUERUD?XVU�?Y\XND?SHOLNDQ?�?