Ja Min Jeong

2013/03/22

Korea University

Computer Graphics Lab.

Jing Liao · Jinhui Yu

Visual Computer 2012

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 2 KUCG |

Abstract

• For animating cracks and fractures

Input • a 2D hand drawn object

• Minimum user intervention

Generate cartoon cracks and fractures animations procedurally • Generate the Voronoi textures on the 2.5D object model

‗ Visual abstraction of cartoon cracks

• Cracking gaps are widened progressively until Voronoi cells split apart

• Fall onto ground according to simplified physical rules

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 3 KUCG |

Overview

Result

Algorithm Overview

Input Image and User Intervention

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 4 KUCG |

1. Introduction

• Animating cartoon crack

Requires animators to draw many broken pieces in a frame

Animate them with multiple frames in a visually convincing manner

Hand-drawn crack and fracture effects

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 5 KUCG |

1. Introduction

• Some approaches of physically based modeling of crack fractures on 3D objects

These methods focus on realistic effects

Cannot be used straightforwardly in cartoon animation because of inconsistency in visual style

We have to seek for different solutions to animate crack fractures in cartoon style, using just 2D painted objects and the background

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 6 KUCG |

1. Introduction

• Pursuing this goal therefore imposes the following challenges different from those in 3D realistic crack fracture animation

1. It is very difficult to reconstruct 3D models from 2D cartoon drawings in general

2. Introduce 3D information such as thickness to broken shapes

3. Object shadows on the background

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 7 KUCG |

2. Related work

• Physical approach Crack patterns

• Hirota et al. ‗ Crack in surface ‗ Crack in volume

• Gobron and Chiba ‗ Cellular automata

• Paquette et al. ‗ Paint cracking and peeling were also simulated using a two-layered

model on a 2D grid

• Federl and Prusinkiewicz ‗ Wedge-shaped finite elements ‗ Model cracks formed by drying mud and tree bark

• Iben and O’Brien ‗ Finite elements method ‗ Generate cracks from a stress field

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 8 KUCG |

2. Related work

• Physical approach

Simulate objects that are being broken or torn apart • Terzopoulos et al

‗ elastic deformation with mass–spring systems

• Terzopoulos and Fleischer ‗ plastic deformation and fracture

‗ spring stretches beyond its elastic limit, it breaks

• Norton et al & Mazarak et al ‗ similar approaches by attaching voxels together with springs

‗ local pressure or force exceeds a designated yield limit

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 9 KUCG |

2. Related work

• Physical approach

Mass–spring systems, Finite Elements Method • Brittle fracture

• Ductile fracture

• Elasto-plastic materials & Interactive fracture

• Fracture and deformation of voxelized surface meshes

Other algorithms • Generating fracture on elastic and plastic materials with

the virtual node algorithm

• A membrane-bending model for thin shell objects

• A meshless framework

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 10 KUCG |

2. Related work

• Non-physical approach • Physical models

‗ be slow and difficult to control

• Non-physical models ‗ Quicker and easy to control

Voronoi-based methods ‗ Crack : Voronoi boundaries ‗ Progress of a crack : Voronoi network

Raghavachary Mould Wyvill et al.

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 11 KUCG |

3. Surface and volume approximation

• Our system the input object is drawn on 2D

• Just breaking the drawn object into 2D broken pieces could not show the volumetric appearance

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Ja Min Jeong | 2013/03/22 | # 12 KUCG |

3. Surface and volume approximation

• Construct the front and back half of the input object to approximate its surface area instead.

• This region is assigned the color of the original image on the non-shadow region

Fig. 3 2.5D model of the input object

FH : front half BH : back half

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Ja Min Jeong | 2013/03/22 | # 13 KUCG |

3. Surface and volume approximation

• Two images of FH and BH are stored in two layers with depth order assigned as a 2.5D model

• Hand-drawing many broken pieces involved in cartoon crack fractures

• Reduces the animator’s workload Interactive segmentation and construction of FH and BH

• Volumetric appearance Introduce thickness to FH and BH (Sect. 6.)

Fig. 7 Modeling 3D fragment

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Ja Min Jeong | 2013/03/22 | # 14 KUCG |

4. Voronoi textures

• Voronoi diagram to simulate crack textures appearing in hand-drawn crack fractures

• VP(pi) : defined to be the set of all points q in the plane for which pi is among the closest point to q in P

P : Points N : Number

VP(pi) : Voronoi polygon VD(pi) : Voronoi Diagram

Fig. 4 Voronoi diagram (solid) and Delaunay triangulation (dot)

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 15 KUCG |

4. Voronoi textures

• Algorithms for constructing the Voronoi diagram

Adopt the simple algorithm by Lischinski • The incremental construction of the Delaunay triangulation

and the Voronoi diagram

Synthesize a Voronoi diagram on two layers of FH and BH

The VD(P ) constructed above only models underlying structures of the cartoon crack fractures

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 16 KUCG |

5. Modeling cracking

• Cracking is a process that usually starts from some positions where the object is hit cracks advance on the object (crack advancing) Gaps of cracks widen progressively (gap widening)

Fig. 5 Algorithm of dynamic cracking texture

1. Several Voronoi vertices are chosen by the user as activating seeds

2. The cracking line zigging along its corresponding edge at a certain speed

3. When a cracking line reaches an inactivated vertex 1. Became a new activating seed

2. Trigs more cracking lines

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Ja Min Jeong | 2013/03/22 | # 17 KUCG |

5. Modeling cracking

• Cracking propagation process terminates All cracking lines have reached the contours

Vertices activated previously

• Crack widening The earlier emerged crack lines are wider than those new ones

Model this by assigning age to the cracking line width • The older, The wider

• Cracks animating starts FH BH

Fig. 6 Cracking texture animated in three different frames

line widening W0 : the initial width W : speed t : time.

L0 : the initial length L : speed t : time.

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 18 KUCG |

6. Modeling fracturing

• Second phase begins When cracking lines transverse the whole object Object shatters into small fragments which then fall on other objects

such as floor and ground

• During the falling period Fragments may interact with each other under the gravity Causing rotation, Collision and Piling up Fragments are just 2D shapes of Voronoi cells

• Can not be used realistic rotations, collision and piling up of fragments

• Add thickness to each fragment Construct a 3D fragment by copying a Voronoi cell Move it along the direction of the cell normal to a distance denoted by d

• equals the thickness of the fragment specified by the user

Fig. 7 Modeling 3D fragment

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 19 KUCG |

6. Modeling fracturing

• Thickness of the fragments Should be increased so that they appear reasonably bigger

than the thinner fragments derived from some objects such as bowls

Simply increased the thickness of fragments • Center : d, Size : 1.5d

• All fragments Are made of the same materials and the same density Fall as the solid bodies to the ground plane under gravity Elastic collision or inelastic collision according to the material

defined

• Implementation Fragments falling, colliding and piling up Physx library

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 20 KUCG |

6. Modeling fracturing

• No 3D information available For calculating the collision between falling fragments

and the ground Set up a virtual 3D ground plane

• Physx Set some mechanical characteristics

• Density of the object • Gravity • Restitution parameter • Friction parameter

The position of every fragment in each frame Colliding detection

• If you want to speed up : using bounding box

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 21 KUCG |

7. Treatment of shadows

• Shadows of broken objects

Cracking phase • Objects just begin to crack

• Objects still remain their shapes

• No shadow animation is required

Fracturing phase • Objects break down into pieces

• Shadows of broken pieces vary as they fall

• Shadow animation can be done with the traditional shadow map algorithm

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 22 KUCG |

8. Result

• 2.5 GHz Pentium PC with 2048 MB of RAM.

• Microsoft Visual C++ and OpenGL Libraries.

Fig. 8 Cracking and fracturing of a bowl

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 23 KUCG |

8. Result

Fig. 9 Cracking and fracturing of a house

8 Frame

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 24 KUCG |

8. Result

Fig. 10 Cracking and fracturing of a cartoon character

Material : Mud

Korea University Computer Graphics Lab.

Ja Min Jeong | 2013/03/22 | # 25 KUCG |

9. Conclusion

• Present a theme of modeling cracking and fracturing effects for cartoon animation

• The first attempt to model cracking and fracturing effects for 2D cartoon objects

• Limitation

Cannot be seen from arbitrary views in 3D • only reconstruct the 2.5D model for cartoon objects