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Shape Forming by Cutting and Deforming Operations Koichi Hirota, Atsuko Tanaka, Toyohisa Kaneko, Michitaka Hirose Proc. ICAT 2000, 19-24, 2000.10 9217005 黃琬婷 2007.1.2 OUTLINE Introduction Deformation Operation Tearing Operation Cutting Operation Conclusion Introduction GOAL Provide the direct manipulation interface for deforming and cutting operations. Simulate cutting and deforming operations with force feedback. Implement a virtual modeling environment. Introduction Motivation Physically based modeling and simulation is desirable 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. Introduction Background-1 Free Form Deformation Free-Form Deformation of Solid Geometric Models; SIGGRAPH ’86, pp.151-161, 1986. approach can’t represent force Control-point based can’t direct operation Geometric Direct Deformation Method A Direct Deformation Method; Proc. VRAIS’93, pp.499-504, 1993. Can’t compute the interaction force. Must combine other model that can compute inter-force. Introduction Background-2 Combine physically based model model slow, hard to real-time Linear FEM model bad for large deformation Spring-Network model higher update rate Network of spring is constructed along edges of the polygon model The result of the simulation is reflected on the precise geometry model. FEM Introduction 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 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 Operation 根據施力計算spring network 的變形量 受力超過彈簧承受值的端 點與邊便分開 根據spring network的狀況 分離代表object的四面體 並計算應有的形變量 Tearing Operation Cutting 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. Geometrical 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 : 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. 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 Operation Sculpturing operation Cutting Operation Sculpturing operation Cutting 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. Geometrical 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 : 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. 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 Operation Geometrical cutting operation Boolean operation Polygon model Suppose object A and a locus of cutting device B are defined. The object after cutting is represented by A AND (NOT B) Cutting 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. Cutting Operation 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)]. Cutting Operation Geometrical cutting operation - result Cutting Operation Geometrical cutting operation - result Cutting Operation 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. Cutting 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 fed back to the operator was determined only from the velocity of cutting the object. Geometrical 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 : 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. 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 Operation Computation of Cutting Force Geometric Cutting Cutting Operation 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. Cutting Operation 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. Cutting Operation Computation of Cutting Force Fractional force (摩擦力) Cutting resistance (切割阻力) Represent the friction between the cutting edge and the object. Does not contribute to cutting The part of the material is destroyed when the shearing force exceed 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 Operation Computation of Cutting Force Operation of Cutting Tool: Calculate force : 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. 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. Cutting Operation 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. Cutting Operation 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 Cutting Operation Geometric Cutting The shape consisting of 6000 tetrahedral is colliding with the trajectory surface consisting of 18 polygons and took about 4 seconds for the geometric processing. Conclusion 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.