Volume Animation. Introduction Introduction The computer graphics by the volume can easily construct the amorphous object and the translucent object

Volume AnimationVolume Animation

IntroductionIntroduction

The computer graphics by the volume can easily construct the amorphous object The computer graphics by the volume can easily construct the amorphous object and the translucent object.and the translucent object.

And, it is able to visualize without doing modeling from the slice data of a And, it is able to visualize without doing modeling from the slice data of a medical image, and so on. But, the processing time is very slow because the data medical image, and so on. But, the processing time is very slow because the data size is bulky. size is bulky. It is difficult to express the dynamically deformed object by It is difficult to express the dynamically deformed object by animationanimation

Three methods for volume animation are described at the following. Three methods for volume animation are described at the following. It is the method of the high speed rendering in the amorphous object,It is the method of the high speed rendering in the amorphous object, The method of operation, which dynamically bends the joint, The method of operation, which dynamically bends the joint, and the arbitrary deformation method.and the arbitrary deformation method.

Fast Volume Rendering and Animation of Fast Volume Rendering and Animation of Amorphous Phenomena Amorphous Phenomena

When the amorphous phenomena are used in the real time application, a speed When the amorphous phenomena are used in the real time application, a speed and persuasive realism are necessary, such as convincing interactive and persuasive realism are necessary, such as convincing interactive environments, gaseous effects. The performance of the system depends on the environments, gaseous effects. The performance of the system depends on the resolution of volume grid. resolution of volume grid.

An approach discussed is based on the efficient splatting algorithm, coarse and An approach discussed is based on the efficient splatting algorithm, coarse and regular voxel grid of opacity values.regular voxel grid of opacity values.

In splatting algorithm, the volume is thought of as a field of overlapping In splatting algorithm, the volume is thought of as a field of overlapping interpolation kernels interpolation kernels hh..

Such kernel is placed at each voxel location Such kernel is placed at each voxel location j j and weighted by the voxel's value and weighted by the voxel's value vvjj. .


The volume rendering can be thought as the process of casting viewing rays into The volume rendering can be thought as the process of casting viewing rays into the volume and integrating the volume along these rays. the volume and integrating the volume along these rays.

Ray casting calculates an integral by sampling the volume along the ray and Ray casting calculates an integral by sampling the volume along the ray and composing the samples in front to back order. This sampling operation is composing the samples in front to back order. This sampling operation is expensive, and a voxel may be involved in many such sampling operations, expensive, and a voxel may be involved in many such sampling operations, depending on the sampling distance.depending on the sampling distance.


On the other hand, splatting provides a more efficient way to generate the ray On the other hand, splatting provides a more efficient way to generate the ray integral. integral.

It is realized by simplifying the volume integral and separation a single voxel It is realized by simplifying the volume integral and separation a single voxel vvjj, ,

and kernels and kernels hh..

where where ss is the integration of the interpolation kernel in the direction of the is the integration of the interpolation kernel in the direction of the viewing ray. If the viewing direction is constant for all voxels or if the viewing ray. If the viewing direction is constant for all voxels or if the interpolation kernel is radially symmetric function, then we may pre-integrate interpolation kernel is radially symmetric function, then we may pre-integrate into a lookup tableand use this table for all voxels. into a lookup tableand use this table for all voxels.

Then, this approach uses anisotropic interpolation kernels that are neither Then, this approach uses anisotropic interpolation kernels that are neither monotonic nor smooth, but rather fractal-like nature.monotonic nor smooth, but rather fractal-like nature.

dsshV j )(

dssh )(


The algorithm consists of the following stepsThe algorithm consists of the following steps

1. Select a set of textures to represent the volume and create the kernels footprint 1. Select a set of textures to represent the volume and create the kernels footprint tabletable

2. Create a volume out of regularly spaced voxels2. Create a volume out of regularly spaced voxels

3. Assign an initial texture to each voxel3. Assign an initial texture to each voxel

4. Render the current frame by drawing the volume in back to front order4. Render the current frame by drawing the volume in back to front order

5. Assign new textures to each voxel5. Assign new textures to each voxel

6. Repeat 4-56. Repeat 4-5


Step 4 and 5 are done for every frame for animation.Step 4 and 5 are done for every frame for animation. In step 1, the set of textures which contain the frequencies, is converted to In step 1, the set of textures which contain the frequencies, is converted to

grayscale and windowed with an optimal kernel footprint function. Figure grayscale and windowed with an optimal kernel footprint function. Figure illustrates how a textured splat is constructed from texture (left picture) and a illustrates how a textured splat is constructed from texture (left picture) and a kernel footprint (right picture).kernel footprint (right picture).


Step 2 is to represent the overall shape of the effect as a regular voxel grid. Step 2 is to represent the overall shape of the effect as a regular voxel grid. In step 3, the voxels are given an initial textured kernels. In step 3, the voxels are given an initial textured kernels. In step 4, drawing each voxel's weighted kernels in a back to front order with In step 4, drawing each voxel's weighted kernels in a back to front order with

respect to the viewpoint, renders the volume. respect to the viewpoint, renders the volume. Finally, in step 5, a new texture is selected for the next frame.Finally, in step 5, a new texture is selected for the next frame.

Clustering and Deformation. Volume Clustering and Deformation. Volume AnimationAnimation

The objective is to accurately model interior information of volumetric objects The objective is to accurately model interior information of volumetric objects for animation of physical behavior. Therefore, the entire shape is decided in for animation of physical behavior. Therefore, the entire shape is decided in each blocked parts of the volume, and the volume data is put on the block. each blocked parts of the volume, and the volume data is put on the block.

The method consists of the following step. The method consists of the following step.

1. The input volume data is loaded into the system as a single volume texture 1. The input volume data is loaded into the system as a single volume texture (voxture). (It mean as a volume data)(voxture). (It mean as a volume data)

2. Cluster a input voxture. Clustering is used to separate segments of the volume. 2. Cluster a input voxture. Clustering is used to separate segments of the volume. The clustered volume is done to obtain the blocks which represent each segment The clustered volume is done to obtain the blocks which represent each segment of the volume.of the volume.

3. The blocks are deformed using the finite element method (FEM).3. The blocks are deformed using the finite element method (FEM).

4. The voxture is mapped to the deformed blocks. 4. The voxture is mapped to the deformed blocks.

5. Render volume.5. Render volume.

6. Repeat 3-5.6. Repeat 3-5.


The functional modules used for generation the animation by clustering The functional modules used for generation the animation by clustering and deformation and deformation


The visible human example is voxture-mapped into the block The visible human example is voxture-mapped into the block representation of the human as shown in Figure. representation of the human as shown in Figure.

The initial block specification of the human was obtained interactively The initial block specification of the human was obtained interactively from the original sleeping posture of the volume dataset.from the original sleeping posture of the volume dataset.

In the visible human example, in order to animate the human, we have to In the visible human example, in order to animate the human, we have to separate the hands and torso. separate the hands and torso.

After the clustering is applied to the visible human data, we obtain a After the clustering is applied to the visible human data, we obtain a dataset with two clusters. dataset with two clusters.


One cluster represents the voxels of the hands and the other the voxels One cluster represents the voxels of the hands and the other the voxels that belong to the torso.that belong to the torso.

Figure shows the volume clustering. Figure shows the volume clustering.


Next, the clusters are sampled separately to obtain a number of Next, the clusters are sampled separately to obtain a number of polyhedral blocks.polyhedral blocks.

Figure illustrates the sampled blocks for the hand cluster and the body Figure illustrates the sampled blocks for the hand cluster and the body cluster.cluster.

Skeleton Tree Volume AnimationSkeleton Tree Volume Animation

The method consist of thinning the volume using a parameter controlled The method consist of thinning the volume using a parameter controlled volume thinning algorithm and then connecting the thinned voxels into a volume thinning algorithm and then connecting the thinned voxels into a skeleton tree. skeleton tree.

The skeleton tree is a simple shape which is easier to manipulate The skeleton tree is a simple shape which is easier to manipulate compared to the entire volume data. The shortest distance from a skeletal compared to the entire volume data. The shortest distance from a skeletal voxel to the object boundary is stored and used to reconstruct the object, voxel to the object boundary is stored and used to reconstruct the object, termed the distance transform. termed the distance transform.

The deformed object can be reconstructed from the deformed skeleton The deformed object can be reconstructed from the deformed skeleton tree by distance transform.tree by distance transform.


The volume is thinned using a parameter controlled skeletonisation The volume is thinned using a parameter controlled skeletonisation algorithm. The algorithm takes a segmented volume as input and extracts algorithm. The algorithm takes a segmented volume as input and extracts a thinned subset called the skeleton. a thinned subset called the skeleton.

A thinness parameter (TP) is used to select voxels that belong to the A thinness parameter (TP) is used to select voxels that belong to the skeleton (higher values yield a thinner skeleton). skeleton (higher values yield a thinner skeleton).

Deformation of a volume can be achieved by rotation of its skeleton tree Deformation of a volume can be achieved by rotation of its skeleton tree parts about a control point or by transformation, by scaling, by parts about a control point or by transformation, by scaling, by disconnecting the skeleton tree, or etc.disconnecting the skeleton tree, or etc.

In the Reconstruction, the deformed volume is reconstructed from the In the Reconstruction, the deformed volume is reconstructed from the deformed skeleton tree. deformed skeleton tree.


Figure illustrates an example of the skeleton tree and the corresponding Figure illustrates an example of the skeleton tree and the corresponding reconstruction for two different thinness values. reconstruction for two different thinness values.

Examples. Emulating Human Examples. Emulating Human Face MotionFace Motion

Examples. Emulating Human Examples. Emulating Human Face MotionFace Motion

Data of 150x200x192 voxels is used. We apply trilinear Data of 150x200x192 voxels is used. We apply trilinear interpolation to it and subtract a given level value to interpolation to it and subtract a given level value to define the continuous function. Figure (b) shows how the define the continuous function. Figure (b) shows how the skin layer is acted upon by the muscle layerskin layer is acted upon by the muscle layer

chew.mpegchew.mpeg

Particle SystemsParticle Systems

Newtonian particle systemsNewtonian particle systems

A particle is described by its mass, m, and its A particle is described by its mass, m, and its trajectory, trajectory, rr(t), as illustrated in Figure(t), as illustrated in Figure

Newtonian particles are the most common and are Newtonian particles are the most common and are governed by Newton’s second lowgoverned by Newton’s second low

FF = m = mdd2rr((tt)/)/dtdt22,

where r(t) = [x1,x2,x3]T is the position of a particle at time t and a(t) = dd2rr((tt)/)/dtdt22 is the instantaneous acceleration of the particle.

Newton’s second law is converted into two coupled first-order differential equations where a point p R6 in phase space is denoted by its position r and velocity v = ddrr((tt)/)/dtdt


Explicit Euler solutions to ordinary differential Explicit Euler solutions to ordinary differential equations are very simple to implement.equations are very simple to implement.

However, they are neither stable with respects to However, they are neither stable with respects to large steps,large steps, h h, nor very accurate. See, Figures, nor very accurate. See, Figures

Figure (a) shows the iso-energy values of a Figure (a) shows the iso-energy values of a rotational symmetric system. rotational symmetric system.

Assuming that the speed is initially zero, then the Assuming that the speed is initially zero, then the correct solution would be the particular circle that correct solution would be the particular circle that the particle was positioned on initially.the particle was positioned on initially.

Instability is demonstrated in Figure (b)Instability is demonstrated in Figure (b)


Verlet [Verlet, L., 1967, Computer “experiments” Verlet [Verlet, L., 1967, Computer “experiments” on classical fluids. I. Thermodynamical properties on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Physical Rivew, of Lennard-Jones molecules, Physical Rivew, 159(1), pp. 98-103] proposed a scheme where 159(1), pp. 98-103] proposed a scheme where velocity is represented implicitly by the previous velocity is represented implicitly by the previous and current positions:and current positions:

rr((tt++hh) = -) = -rr((t-ht-h) + 2) + 2rr((tt) +) + h h22aa((tt) +O(h) +O(h3).). When a particle is found to penetrate an obstacle, When a particle is found to penetrate an obstacle,

then a simple collision response projects out the then a simple collision response projects out the obstacle along the shortest path. See, Figure.obstacle along the shortest path. See, Figure.


Particle systems are conceptually very simpleParticle systems are conceptually very simple There are many systems, that with clever There are many systems, that with clever

applicationsapplications Consider one of them: Consider one of them: Physically-Based Visual Physically-Based Visual

Simulation of CometsSimulation of Comets in Virtual in Virtual Environments Modeling the Solar SystemEnvironments Modeling the Solar System by by D. Yamazaki and D. Yamazaki and V. SavchenkoV. Savchenko

There is a natural curiosity in everything about the Earth and space.

• The system enhances this curiosity through structured activities that help to grasp concrete ideas about space.

Physically-Based Visual Simulation of CometsPhysically-Based Visual Simulation of Comets in in Virtual Environments Modeling the Solar SystemVirtual Environments Modeling the Solar System

MotivationMotivation• One of the more spectacular

changes recorded for comet Halley during an apparition was the detachment event that occurred on April 12, 1986. This 3 minute exposure was taken using the Michigan Schmidt telescope at Cerro Tololo Interamerican Observatory. The resulting image clearly shows part of the ion tail structure detached from the comet. (Courtesy NASA/JPL)


MotivationMotivation

• Simulation of cometary phenomena• Evaporation process• Interaction between the process and the

surrounding environment - Previous work does not consider changes of a cometary

motion

Necessity to consider whole cometary phenomena


Characteristics of a CometCharacteristics of a Comet• Structure

• Nucleus• Coma• Dust tail• Plasma tail

• Evaporation process• Begins inside of Mar’s orbit

Generation coma and two tails

Our Simulation SystemOur Simulation System

Comet Window• Composition of two parts

Virtual Solar System with a moving comet


Virtual Solar SystemVirtual Solar System• Implementation by the use of Java3D• Dynamics Orbital motion - Kepler’s Equation and Orbital elements

- Semi major axis- Time of the perihelion passage- Eccentricity- Longitude of the node- Inclination- Argument of perigee- Position and velocity data of the famous comets

Comet spinning about some axis- Direction of the axis and the angular velocity remains constant

• Visualization Planets - spheres mapped with their own texture Comets - physically based particle simulation


Graphical User InterfaceGraphical User Interface

• Start / Stop

• Speed

• View Angle

• Zoom

• Orbital elements

• Rendering method• Parallel projection or Volume visualization

• Selection of famous comets• Comet Halley on May 27,1911


Particle FlowParticle Flow• Evaporation Process ((Whipple’s theoryWhipple’s theory))

rk : the position vector of the nucleusvk : the velocity vector of the nucleusρi : boundary of the expansion zonewi : the final thermal velocity

• Free flying Process

f i : repulsive factor μ : the gravitational constant


Rendering (1)Rendering (1)

• Parallel Projection

• Fast

• Inferior to realistic

Rendered by parallel projectionNekoAnimation\Cometaimage2.html

Simple mapping particles onto the screen


Rendering (2)Rendering (2)• Volume Visualization

• Realistic image

• Time consuming

Voxel density Color density Transparency

Particle density

Ray tracing through the volume data


Comet moving near the Sun

ResultsResults• The orbital elements of Comet Halley in 1986

Documents

Volume Animation. Introduction Introduction The computer graphics by the volume can easily construct the amorphous object and the translucent object