Developmental Models of Herbaceous Plants for Computer Imagery Purposes

Transcription

1 Developmental Models of Herbaceous Plants for Computer Imagery Purposes P. Prusinkiewicz, A. Lindenmayer, J. Hanan Proc. SIGGRAPH 1988

2 Overview Introduction Branching Structures Plant Development Geometrical Interpretation Developmental Models Modeling Organs Christopher Clement 2

3 Introduction Goal: Model herbaceous plants suitable for: Generating realistic plant images Animate developmental processes Realism: Simulate plant growth mechanisms L-systems: Models plant architecture, leaves, and flowers Christopher Clement 3

4 Branching Structures Rooted Trees Axial Trees Christopher Clement 4

5 Rooted Trees Labeled, Directed Root Node Terminal Nodes Edges Branch Segments Terminal Segments Christopher Clement 5

6 Axial Trees A type of rooted tree Each node has: At most one straight segment Zero or more lateral (side) segments Axis: Starts at root or lateral segment Rest composed of straight segments Last segment not followed by any straight segment Christopher Clement 6

7 Axial Trees (cont.) Christopher Clement 7

8 Plant Development Achieved via an edge rewriting mechanism Tree Productions: replace an edge (predecessor) with an axial tree (successor) Context-free Context-sensitive: consists of a left context, right context, and strict predecessor Productions applied in parallel Christopher Clement 8

9 Plant Development (cont.) Christopher Clement 9

10 Plant Development (cont.) Christopher Clement 10

11 L-systems A parallel rewriting system Can be deterministic or non-deterministic String representation consists of: Edge labels Brackets [ and ], which denote branches Context sensitive productions have the form: L < S > R Christopher Clement 11

12 L-system Examples Represented by ABC[DE][SG[HI[JK]L]MNO] Matches a production with predecessor BC < S > G[H]M Christopher Clement 12

13 L-system Examples (cont.) ω : S ω : A p 1 : S S[S]S[S]S p 1 : A S[A]S[A]A p 2 : S SS T 0 :S T 1 : S[S]S[S]S T 2 : S[S[S]S[S]S]S[S]S[S]S[S[S]S[S]S]S[S]S[S]S T 0 : A T 1 : S[A]S[A]A T 2 : SS[S[A]S[A]A]SS[S[A]S[A]A]S[A]S[A]A Christopher Clement 13

14 L-system Examples (cont.) Christopher Clement 14

15 L-system Examples (cont.) ω : J[I]I[I]I[I]I p 1 : J < I J ω : I[I]I[I]I[I]J p 1 : I > J J T 0 : J[I]I[I]I[I]I T 1 : J[J]J[I]I[I]I T 2 : J[J]J[J]J[I]I T 3 : J[J]J[J]J[J]J T 0 : I[I]I[I]I[I]J T 1 : I[I]I[I]J[I]J T 2 : I[I]J[I]J[I]J T 3 : J[I]J[I]J[I]J Christopher Clement 15

16 Geometrical Interpretation Generate 3D image from L-system string Symbols interpreted as commands to maneuver a LOGO-like turtle Turtle maintains state: Position Orientation: heading (H), left (L), up (U) vectors Other attributes (current color, line width, etc.) Christopher Clement 16

17 Moving the Turtle Symbol segment symbol + - ^ & \ / Action move forward a distance d while drawing turn left around U by angle increment δ turn right around U by angle increment δ turn 180 around U pitch up around L by angle increment δ pitch down around L by angle increment δ roll right around H by angle increment δ roll left around H by angle increment δ [ push current state onto stack ] pop state from stack; set as current state Christopher Clement 17

18 Interpretation Example Additional symbols: ': increment color table index!: decrease diameter of segments Christopher Clement 18

19 Developmental Models Sequential Growth Delays Qualitative Changes Interactions Signals Model Variation Christopher Clement 19

20 Sequential Growth An indefinite number of flowers are produced sequentially from a single stem Christopher Clement 20

21 Sequential Growth (cont.) Similar effect: leaves on zero and first order axes Christopher Clement 21

22 Delays Model delayed growth with additional states Christopher Clement 22

23 Qualitative Changes Change development at a point in time Christopher Clement 23

24 Qualitative Changes (cont.) Modeled via: Delay Mechanism Stochastic Mechanism Environmental Change Christopher Clement 24

25 Interactions via Signals Use signals to time developmental switches Christopher Clement 25

26 Model Variation Introduce variation into plants generated by deterministic L-systems In this case, π 1, π 2, and π 3 = 1/3 Christopher Clement 26

27 Modeling Organs Account for surfaces and volumes Simplest approach: predefine models Requires stages to be modeled individually Other approaches: Fill polygons consisting of L-system lines Define additional edges Christopher Clement 27

28 Modeling Organs (cont.) Fill polygon defined between { and }. Christopher Clement 28

29 Modeling Organs (cont.)? and # define the endpoints of new edges to be added. Christopher Clement 29

30 Any Questions? Christopher Clement 30