shape forming by cutting and deforming operations shape forming by cutting and deforming operations...

Shape Forming by Cutting aShape Forming by Cutting and Deforming Operationsnd Deforming Operations

Koichi Hirota, Atsuko Tanaka, Toyohisa Kaneko, Michitaka Hirose

Proc. ICAT 2000, 19-24, 2000.10

9217005 9217005 黃琬婷黃琬婷2007.1.22007.1.2

OUTLINEOUTLINE

IntroductionIntroductionDeformation OperationDeformation OperationTearing OperationTearing OperationCutting OperationCutting OperationConclusionConclusion

IntroductionIntroduction

GOALGOALProvide the direct manipulation interface for

deforming and cutting operations.Simulate cutting and deforming operations

with force feedback.Implement a virtual modeling environment.


MotivationMotivationPhysically based modeling and simulation is d

esirable to increase reality.Problem：

Physically based models requires more computation cost than geometrical models.

Hard to real-time!!

Solution:Use two models of different complexity for physical and geometric simulations.


Background-1Background-1Free Form Deformation

Free-Form Deformation of Solid Geometric Models; SIGGRAPH ’86, pp.151-161, 1986.

Geometric approach can’t represent forceControl-point based can’t direct operation

Direct Deformation Method A Direct Deformation Method;

Proc. VRAIS’93, pp.499-504, 1993.

Can’t compute the interaction force.

Must combine other modelthat can compute inter-force.


Background-2Background-2Combine physically based model

FEM model slow, hard to real-timeLinear FEM model bad for large deformationSpring-Network model higher update rateNetwork of spring is constructed along edges of

the polygon modelThe result of the simulation is reflected on the

precise geometry model.


Main Idea The shape of objects are defined

as a collection of tetrahedral elements. Surface shape is represented by a geometric model Physical reaction is simulated using a spring model. The deformation of the spring model is reflected onto

the geometric model by using the interpolation technique.

Deformation OperationDeformation Operation A spring network that covers a

cubic area is created.

spring cells that is out of the object volume is deleted.

根據使用者操作算出作用於彈簧模型上的力 .Deform cells.

由幾何模型的內插方法 Deform objects.

Tearing OperationTearing Operation 根據施力計算根據施力計算 spring netwspring netw

ork ork 的變形量的變形量

受力超過彈簧承受值的端受力超過彈簧承受值的端點與邊便分開點與邊便分開

根據根據 spring networkspring network的狀的狀況分離代表況分離代表 objectobject的四面的四面體並計算應有的形變量體並計算應有的形變量

Tearing OperationTearing Operation

Cutting OperationCutting Operation Sculpturing operation

Galyean T.A.: Sculpting: An Interactive Volumetric Modeling Technique, Computer Graphics, vol.25, no.4, pp.267-274, 1991.

Voxel-based model was used to define the shape Force feedback to the operator was determined only from the velocity of

cutting the object. Yamamoto K., Ishiguro A., Uchikawa Y.: A Development of Dynamic Deforming Algorithms for 3D Shape Modeling with Generation

of Interactive Force Sensation; Proc. VRAIS ’93, pp.505-511, 1993.

Geometrical cutting operationGeometrical cutting operation Tanaka A., Hirota K., Kaneko T.: Virtual Cutting with Force Feedback; Proc. VRAIS ’98, pp.71-75, 1998.

Boolean operation on the polygon-based model Force feedback :

Our method Coarse physical model and fine geometric model and combined

them with each other. Fast update rate of physical simulation for force feedback Precise representation of geometric shape

Cutting OperationCutting Operation

Sculpturing operation



Voxel-based model was used to define the shape Force feedback to the operator was determined only from the velocity of



Geometrical cutting operationGeometrical cutting operation Tanaka A., Hirota K., Kaneko T.: Virtual Cutting with Force Feedback; Proc. VRAIS ’98, pp.71-75, 1998.


Our method Coarse physical model and fine geometric model and combined



Geometrical cutting operation Boolean operation Polygon model Suppose object A and a locus of

cutting device B are defined. The object after cutting is repres

ented by A AND (NOT B)

Cutting OperationCutting Operation Geometrical cutting operation

Our objects of interest and the cutting device given in solid models are all converted into a set of triangular patches with normal directions indicating the external direction.


Geometrical cutting operation Cutting friction increases in proportion to the velocity

of the cutting blade. Checking whether all the polygons (triangles) interact

with the straight lines. If no interaction, the force = 0 If an interaction exists,

be its present position be its position at a cycle prior. is a cycle and is set to be 1[ms] k is a constant between force and

speed and is set to be 0:2N/(m/s)].


Geometrical cutting operation - result


Geometrical cutting operation Contribution

With the availability of the force feedback, cutting can be performed more intuitively than with visual feedback alone.

The feedback of force may be used to reduce the effect of sway and stabilize the cutting motion.

Future Work Extend with a device with torque feedback. For the

representation of torque, we need to define the distribution of force on the edge and sides of cutting tool.

The simulation of cutting soft materials that deform during the operation.



Voxel-based model was used to define the shape Force fed back to the operator was determined only from the velocity of



Geometrical cutting operation Tanaka A., Hirota K., Kaneko T.: Virtual Cutting with Force Feedback; Proc. VRAIS ’98, pp.71-75, 1998.


Our methodOur method Coarse physical model and fine geometric model and combined



Computation of Cutting ForceGeometric Cutting


Computation of Cutting Force Define the cutting edge as

a finite set of discrete edges. Each discrete edge holds the

position of two points. One is the position where the cutting edge collides with the

deformed object. The other is the position where the cutting edge collides with

the object in a non-deformed state.

Deformation of the object on each discrete edge is calculated as the disparity between those positions.


Computation of Cutting Force We assume that the force affecting on a discrete edge is

proportional to the displacement at the point where the discrete edge collides with the object.

By computing the force on each discrete edge, we obtain the approximate distribution of force on the edge.

Discrete edges are independent of each other. Updating the position of the colliding point based on the

force affecting the discrete edge.


Computation of Cutting Force Fractional force (摩擦力 )

Represent the friction between the cutting edge and the object. Does not contribute to cutting

Cutting resistance (切割阻力 ) The part of the material is destroyed when the shearing force e

xceed the maximum shearing force that the material can bear.

Viscous drag (黏滯曳力 ) It is proportional to the velocity of the cutting edge.

Cutting OperationCutting Operation Computation of Cutting Force

Operation of Cutting Tool: The position of the discrete cutting edge (Pi) is updated

according to the operation of the cutting tool by the user, and the force on the edge is calculated.

Calculate force : Fractional force Cutting resistance Viscous drag

Feedback Force : Calculate the force on each discrete edge as the sum of the

three forces discussed above The cutting edge moves toward Pi to the closest point

at which it can stably exist without cutting the material.


Geometric Cutting The geometric change caused by the cutting

operation is represented by dividing tetrahedral colliding with the trajectory of the cutting edge.

The proposed algorithm provides a fast method to compute intersection between the cutting edge and the object approximately.


Geometric Cutting 紀錄軌跡分割三角形分割物體更新相鄰關係

The dividing patterns of each tetrahedron


Geometric CuttingThe shape consisting of 6000 tetrahedral is

colliding with the trajectory surface consisting of 18 polygons and took about 4 seconds for the geometric processing.

ConclusionConclusion

We proposed an approach to realize cutting and deforming operations with force feedback.

We defined coarse physical model and fine geometric model and combined them with each other.

fast update rate of physical simulation for force feedback the precise representation of geometric shape

By sharing a geometric model in both cutting and deforming operations, it became possible to switch these two operations without the transforming the internal representation of the object.

shape forming by cutting and deforming operations shape forming by cutting and deforming operations...

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