Interactive Modeling and Authoring of Climbing Plants

Transcription

1 Copyright of figures and other materials in the paper belongs original authors. Interactive Modeling and Authoring of Climbing Plants Torsten Hadrich et al. Eurographics 2017 Presented by Qi-Meng Zhang

2 Abstract Interactive modeling of developmental climbing plants with an emphasis on efficient control and plausible physics response Plant is represented by a set of connected anisotropic particles Each particle stores biological and physical attributes that drive growth and plant adaptation to the environment Light sensitivity, wind interaction, physical obstacles Qi-Meng Zhang # 2

3 1 Introduction

4 1 Introduction Dynamic plant model React to the presence of other plants,to varying lighting conditions, and to the scene itself A number of methods have been proposed for realizing adaptive plants L-system [PRUSINKIEWICZ P., LINDENMAYER A./ The algorithmic beauty of plants Springer-Verlag New York 1990] Inverse procedural model [STAVA O et al./ Inverse procedural modelling of trees Comp.Graph.Forum.2014] Competition for resources [RUNIONS A et al./ Modeling trees with a space colonization algorithm Eurographics 2007] Simulated adaptation [PIRK S et al./ Plastic trees: interactive self adapting botanical tree models ACM Trans. Graph. 31, ] Qi-Meng Zhang # 4

5 1 Introduction The difficulty with climbing plants Need consider adaptation to the geometry of the supporting object Previous approaches simulated climbing plants Environmentally sensitive automata [ARVO J et al./ Modeling plants with environment-sensitive automata Ausgraph 1988] Competing particles in voxel space [GREENE N./ Voxel space automata: Modeling with stochastic growth processes in voxel space SIGGRAPH 1989] Represent tendrils as mass-springs [WONG S.-K and CHEN K.-C./ A procedural approach to modelling virtual climbing plants with tendrils Computer Graphics Forum 2015] Control, is a major open problem in plants modeling Most of the existing algorithm focus on standing tree Control by setting input parameters and the initial location of trees Qi-Meng Zhang # 5

6 1 Introduction Contribution We implemented an interactive method that allows for coherent modeling of climbing plants in changing environments and along the entire developmental process of the plant We model climbing plants as dynamic systems that support biologically- and physically-plausible behavior; plants remain flexible and animation-ready during the modeling session We couple plants with wind simulations and model advanced physical effects Bending and breaking of branches We introduce a number of editing operations Plant seeding, dynamic branch placement, removal, and sketching of attractors on support geometry Qi-Meng Zhang # 6

7 2 Related Work

8 2 Related Work Interactive control by positioning attraction Simulate climbing plants by space colonization Simulate tree by space colonization BENES B and Millan E./ Virtual climbing plants competing for space IEEE Proc. of the Comp. Anim.2002 Wojciech Pałubicki et al./ Self-organizing tree models for image synthesis ACM Trans. Graph.2009 Require the entire plant or a set of parameters Simulate plants by either Inverse procedural modeling Simulate plants by simulating the effect of wind on tree development STAVA O et al./ Inverse procedural modelling of trees Comp.Graph.Forum.2014 PIRK S et al./ Windy trees: Computing stress response for developmental tree models ACM Trans. Graph.2014 Qi-Meng Zhang # 8

9 2 Related Work Interactive methods focus on user control Example-based sketching system Integrates many aspects of interactive plant modeling and uses the space colonization algorithm OKABE M et al./ Interactive design of botanical trees using freehand sketches and example-based editing SIGGRAPH Courses.2007 Steven Longay et al./ TreeSketch: Interactive procedural modeling of trees on a tablet SBIM.2012 Climbing plants Used L-system to model -ing climbing plants and react to gravity and sunlight Generate climbing plants with a focus on procedural modeling and the behavior of tendrils that grow around objects KNUTZEN J et al./ Generating Climbing Plants Using L- Systems Master s thesis,chalmers University of Technology.2009 Wong et al./ A procedural approach to modelling virtual climbing plants with tendrils Computer Graphics Forum Qi-Meng Zhang # 9

10 2 Related Work Particle system Integrate spherical particles that approximate a tree structure within a fluid solver to simulate the interaction between trees and wind Simulate deformable object by a meshless approach A. Selino et al./ Large and small eddies matter: Animating trees in wind using coarse fluid simulation and synthetic turbulence Comput. Graph. Forum.2013 MÜLLER M et al./ Meshless deformations based on shape matching ACM Trans. On Graph Simulate deformable solids using SPH(smoothed particle hydrodynamics) Extend shape matching by incorporating oriented particles BECKER M et al./ Corotated sph for deformable solids Eurographics Conf.2009 MÜLLER M et al./ Solid simulation with oriented particles ACM Trans. On Graph Qi-Meng Zhang # 10

11 3 Overview Simulation loop Interaction Update branching structure Particle simulation (Plant dynamic) Geometry-based method Plant growth Directed random walk influenced by environmental conditions Qi-Meng Zhang # 11

12 4 Climbing Plants

13 4 Climbing plants 4.1 Plant dynamic Modifies the existing plant geometry 4.2 Plant growth Add new plant geometry 4.3 Species and Material Properties Qi-Meng Zhang # 13

14 4 Climbing plants Plant module become new leading apex attaches plant to the supporting object Plant skeleton and Branch thickening Figure 3 Qi-Meng Zhang # 14

15 4 Climbing plants 4.1 Plant Dynamics Modifies the existing plant geometry User interactions and external forces Particle-based representation Particle carry quantities for their current state and rest state Position and orientation, main axis(plant skeleton), velocity, angular velocity successor Particle attributes Update in each time step Particle group Include current particle, parent particle, successors current parent Qi-Meng Zhang # 15

16 4 Climbing plants 4.1 Plant Dynamics Our particle-based plant representation is based on the shape matching approach Why need using the shape matching approach? The existing plant shape modified by external forces Like pulling the branches to a different location The shape matching algorithm restores the initial plant shape Eg. pulling Shape matching Qi-Meng Zhang # 16

17 Shape matching algorithm Meshless deformations based on shape matching [MÜLLER M et al./ ACM Trans. 2014] Original shape Deformed shape Matched shape : initial position : actual position : goal position Qi-Meng Zhang # 17

18 4.1 Plant Dynamics Particle Positions Update Particle positions Current position X Predicted position X p Target position X t Goal position X g Figure 4 (a) and (b) Qi-Meng Zhang # 18

19 4.1 Plant Dynamics Predicted Position and Orientation Predicted position X p X : particle position V : particle velocity t: simulation step : gravitational acceleration : external acceleration(caused by fluid particles) Qi-Meng Zhang # 19

20 4.1 Plant Dynamics Predicted Position and Orientation Predicted orientation ω : angular velocity of particle q : current particle orientation Qi-Meng Zhang # 20

21 4.1 Plant Dynamics Optimal Rotation Optimal rotation R Minimizes the RMSD(root mean squared deviation) between two paired sets of points Matches the rest state to the current state of each particle group (polar decomposition) : total moment matrix : symmetric part : particle mass and : current and rest particle positions and : current and rest centers of mass per particle group R = AS 1 Qi-Meng Zhang # 21

22 4.1 Plant Dynamics Optimal Rotation The moment matrix depend on mass m : volume : density a, b, c : the axes of the ellipsoid Qi-Meng Zhang # 22

23 4.1 Plant Dynamics Target and Goal Position Target position Goal position w: individual weight When particle attach to objects Qi-Meng Zhang # 23

24 4.2 Plant Growth Add new plant geometry By using two way Extending existing branches Adding new lateral branches Reacts to environmental conditions Qi-Meng Zhang # 24

25 4.2 Plant Growth Within each time step all particles at the end of the plant s shoots increase their size until a maximal size is reached Growth rate depends on the amount of light at the particle position that can additionally be controlled by the user The two contributions of surface adaption and phototropism are integrated into a new growth position and orientation Qi-Meng Zhang # 25

26 4.2 Plant Growth Surface Adaption Plant particle approaches an object Plant orients itself parallel to the surface Axis: Rotational angle: : vector pointing to the closest surface : current forward vector : controls the surface adaption strength Defined by user Figure 4 (c) Qi-Meng Zhang # 26

27 4.2 Plant Growth Phototropism Plant response to light Orients plant organs towards the light direction Help the apices reach areas with more intensive illumination Axis: Rotational angle: :vector to the light source :light occlusion at the particle location :controls the phototropism response strength Figure 4 (d) Qi-Meng Zhang # 27

28 4.2 Plant Growth Growth Integration Accumulated rotation matrix a returns a rotation matrix Update particle orientation and : current and rest orientations Figure 4 (e) Qi-Meng Zhang # 28

29 4.2 Plant Growth Growth Integration Update particle position In its current state and rest state and :head position :forward vector, Qi-Meng Zhang # 29

30 4.3 Species and Material Properties Branches and Leaves Branches Branching probability Branching variance: [0,1] Direction of lateral branches Thickness of new branch Orientation MAX=90 degrees t c = tp f t c :thickness of child branch t p :thickness of parent branch f :falloff parameter Figure 5 Leaves Model each individual leaf with a single particle Qi-Meng Zhang # 30

31 4.3 Species and Material Properties Stiffness and Branch Breaking Stiffness s : stiffness parameter range from [0,1] Controls the elasticity of plant : s range [0,1] t l : life time t m : time of particle reaches its maximum stiffness Breaking Occur from gravity or user interaction Qi-Meng Zhang # 31

32 5 Authoring

33 5 Authoring 5.1 Dynamic Editing Interactive editing operations Seeding plant anywhere in the scene Add a new shoot from existing branch Grabbing the branches Coupled with fluid dynamics Cutting branches Figure 7 Qi-Meng Zhang # 33

34 5 Authoring 5.1 Dynamic Editing Paint regions on obstacles Attract or repulse the plant s growth New sketch triggers new branch Figure 8 Qi-Meng Zhang # 34

35 5 Authoring 5.2 Collision Response Collision of own organs Particle gets closer to the others than their radius (r n +R n ) Ellipsoid-Ellipsoid Collision Solid simulation with oriented particles [ MÜLLER M., CHENTANEZ N./ ACM Trans. Graph 2011 ] Compute the contact point of two particles and displace them along their normal until they no longer intersect d is the scalar tell us how far to shift ellipsoid x is the contact point x Qi-Meng Zhang # 35

36 5 Authoring 5.2 Collision Response Collision of other plants, obstacles Assign each shape a signed distance field(sdf) Compute the distance of longest axis of a particle and the surface stored in the SDF If the distance is smaller than the length of the longest axis Move the particle SDF: 0 + The sign of 0 represent surface Figure 9 Qi-Meng Zhang # 36

37 5 Authoring 5.3 Two-way Fluid Coupling Couple plants with a fluid simulation Wind field is simulated by Smoothed Particle Hydrodynamics(SPH) : pressure : viscosity Wood and air density: Figure 4 (f) Qi-Meng Zhang # 37

38 5 Authoring 5.3 Two-way Fluid Coupling Fluid quantities,at a certain location x are computed as a weighted sum of neighboring particles j, :volume :smoothing kernel :normalized position vector ( ) Ellipsoidal particles G : linear transformation Qi-Meng Zhang # 38

39 6 Implementation and Result

40 6 Implementation and Result Branch mesh Generate cylinder mesh between two adjacent particles Not explicitly generate a tree graph Shadows Computed by using Variance shadow maps Obstacle collisions Signed distance filed Simulation of fluids and physics response with a time step t = 25ms Qi-Meng Zhang # 40

41 6 Implementation and Result Performance measurements Fig 1 Fig 7 Fig 9 Fig 11 Fig 10 number of particles rendering physics growth collision Fig 14 Qi-Meng Zhang # 41

42 6 Implementation and Result Parameters used for the results Fig 1 Fig 7 Fig 9 Fig 10 Fig 11 Fig 14 N: number of plant B: maximum number of lateral buds BP: branch probability V: branching variance Ph: phototopism Qi-Meng Zhang # 42

43 6 Implementation and Result 6.1 Results Figure 12 Phototropism Figure 12 Gravity and high stiffness Figure 12 Low stiffness Qi-Meng Zhang # 43

44 6 Implementation and Result 6.1 Results Drags Support structure Figure 6 Figure 11 Figure 14 Qi-Meng Zhang # 44

45 6 Implementation and Result 6.2 Evaluation Compare our results to photographs of real climbing plants Real climbing plants Our system Figure 13 Wong et al./ A procedural approach to modelling virtual climbing plants with tendrils Computer Graphics Forum 2015 Qi-Meng Zhang # 45

46 7 Discussion and Limitations Limitation Global control Difficult to predict Species Singleness Biomechanically-plausible simulation Not provide Qi-Meng Zhang # 46

47 8 Conclusion and Future Work Conclusion Our approach Provides an efficient means for the control over plant development Allowing the user to affect growth parameters and physical properties of the plant Handles efficient modeling of external effects Can be induced at any time without prior analysis of the plant structure Provide powerful editing capabilities Allow to modify a plant with respect to its structure and its environment while maintaining a biologically plausible appearance Show the efficiency of our approach on a wide variety of interactive examples Qi-Meng Zhang # 47

48 8 Conclusion and Future Work Future Work First Explore particle-based method and meshless deformation methods with a stronger focus on biological and physical plausibility Second Using particles for the efficient modeling of secondary growth. E.g. development of growth rings, cracking of bark Qi-Meng Zhang # 48

49 Result Video Qi-Meng Zhang # 49