Real time collision detection pdf download

Given 3. Collision Suppose there are n objects in the workspace. The will be checked for all objects at discrete time instants bounding boxes for each object are updated periodically i.

Updated bounding that time instant before the computer graphic images of boxes are checked for interference. For each object with the objects are drawn to the screen. Then, if there is a list of faces for more than one object, a face octree i.

Finally, for each pair of faces that are from separate objects and that inter- sect the same face octree voxel i. In this way, all interfering face pairs are found. Note that the intersec- tion of faces with overlap regions and face octree stages repeatedly test for intersection of a face with an axis- Figure 2. An overlap region. For each pair of objects whose bounding boxes overlap, the inter- section between the two bounding boxes is determined called an overlap region, as shown in Figure 2 and put into a list of overlap regions for each of the two objects.

The overlap regions are passed to the next step. Figure 3. Faces intersecting the overlap region. Once a face of an object is deter- lution for the remaining faces starting from the world mined to be intersecting with at least one overlap region cube of side length L as the root.

To minimize computa- it is placed in a face checklist for the object. If there are tion, only as much of the face octree as is necessary for face checklists for two or more objects, then these are collision detection is built; in particular, a parent node is passed on to the next stage.

Figure 3 shows an example subdivided into its eight children only if it contains faces of faces intersecting an overlap region. The plane equation of the face plane of the second face is then de- termined, and the vertices of the first face are evaluated in it in the same way. If neither face is found to be com- pletely on one side of the face plane of the other face, then more detailed checks are done as follows.

The point of intersection of each edge of face 1 with the face plane of face 2 is found and checked to see if it is inside face 2 a three-dimensional point-in-polygon check—the method used is described in Arvo [] ; if the point is Figure 4. Face pair intersection test. The case where an edge and face plane are coplanar is handled by intersect the parent node are tested for intersection with projecting the edge and face onto the two-dimensional the child nodes.

Also, there is no condensation of the coordinate axis most parallel to the face plane and per- face octree i. If there the projected face and edge. In the same way, the edges are voxels in the face octree, then in each voxel there are of face 2 are checked for intersection with face 1. If no faces from two or more objects. For each voxel, all pos- edges of either face are found to intersect the other face, sible pairs of faces, where the faces are from different then the two faces do not intersect.

However, a face pair is only put into this face pair check- 3. The face pair checklist is then passed to Determination the next stage. Note that it is not necessary to allocate memory and actually build a face octree; faces can simply To determine whether or not a triangular patch be checked for intersection with the standard cubes of an intersects with an axis-aligned box, we perform clipping octree and checked recursively for lower-level cubes against four of the face planes of the faces that comprise thus no memory, beyond the small amount used by the the box; the four face planes are the maximum and mini- stack during recursion, is necessary for storing octrees.

For the final dimen- sion, it is only necessary to check whether or not the remaining vertices of the clipped triangular patch are 3. If either case is true then instant as follows see Figure 4. First, the bounding there is no intersection; otherwise there is intersection. When clipping, whenever the intersec- faces do not intersect.

Examples of experimental objects standardized spheres with different numbers of faces. Finally, before performing any clip- ping at all, two quick tests are done. As a first step, a quick overlap check between the bounding box of the Figure 6. Computation time for each processing cycle for two triangular patch and the axis-aligned box can be done to identical sphere objects with , , , and faces. Sec- ond, the three vertices of the triangular patch can be checked to see if one of them is inside of the axis-aligned box; if so, then the triangular patch and axis-aligned box intersect.

This basic experiment was done with sphere objects having 8, 10, The algorithm and an experimental environment 24, 48, 54, 80, , , , , , , , and were implemented and run on a Silicon Graphics In- faces.

In all experiments described in this section, t 5 72 cycle , when faces from the two sphere objects face octrees were built to resolution level 6. Finally, Figure 7 shows the computation re- approximated by differing numbers of triangular patches quired at the last stage i. Figure 5 shows some of the mum computation and is the true measure of the effi- spheres that were used in the experiments. Computation time at each processing cycle for 15 and for 2 space shuttle objects—collision between two objects is detected at the last cycle.

Figure 7. Computation time at the last stage of the proposed collision detection between two identical sphere objects against the number of planar patches of the objects. The space shuttle experimental object triangular patches. Specifically, 15 identical objects space shuttles with faces—see Figure 9 were moved both translation and rotation motion in the test envi- from two objects were found to be interfering, taking 31 ronment for many processing cycles and the computa- milliseconds of computation.

Figure 8 shows the results tion time required at each cycle to perform collision de- of this experiment. Also in this figure, to provide a basis tection was measured. At the last cycle of the test, faces be colliding, required 16 milliseconds of computation.

Kitamura et al. During the cycles without any collisions, the algo- rithm took negligible rarely more than 5 milliseconds computation time. It increased only when collisions were found. The average computation time for a cycle throughout this experiment was The method detects colliding pairs of faces quite efficiently in a complicated environment; therefore, it is possible to design a virtual object manipu- lation aid using dynamic constraints among faces that provides the user with a natural impression of motion Kitamura, Yee, and Kishino, submitted.

Hardware configuration for interactive experiments. This system offers an environment for teleconferencing with realistic sensa- 4. It cre- Two users participated in the interactive experi- ates an image of a virtual conference room and the re- ment Kitamura and Kishino, Both wore glasses motely located conference participants using computer and gloves with magnetic trackers and manipulated ob- graphics in real time.

The users can work cooperatively jects created by stereoscopic computer graphic images in in the virtual workspace Takemura and Kishino, Figure 11 An example of virtual cooperative work is shown on shows two snapshots from the experiment. The yellow the front cover. In this environment, multiple the motions of the objects, while the orange hand could complicated objects are independently manipulated by change the motions of the objects by touching them. The motions of collided objects are back.

The detected colliding pairs of faces are shown by changed according to the normal vectors of the face their color change to blue, and collision sound is also pairs and their original motion vectors. The objects are generated. Though the mikoshi has faces, it could also reflected at the boundary plane of the environment, present such feedback in real time Miyasato, Ohya, and meaning they continuously moved in the defined envi- Kishino, [video].

The number of faces of Venus, the space shuttle, and each hand was , , and , respectively. Here, a sphere and the hands deformed during motion. Two snapshots from the interactive environment, which includes multiple deformable objects. In general, it is difficult to make such direct comparisons because authors of collision detection pa- pers do not normally give out the code that they used to get their experimental results. Fortunately, however, we found the C language code for the first existing collision detection algorithm in Heckbert , the second exist- ing algorithm is a slight modification of the algorithm proposed in this paper, and the library for the third one is available on the internet.

This algorithm can only be used for convex, rigid objects and it does not return the list of face pairs that are interfering, as ours does. The details of this algo- rithm are given in Heckbert However, briefly, the algorithm works by initially finding a separating plane between each pair of objects. A separating plane is found for two objects by finding the two closest vertices on the objects using the method in Gilbert, Johnson, and Keerth, ; the vector between these two points is Figure Computation time at each processing cycle for the the normal vector of the plane, and the plane passes interactive environment.

If no new sepa- rating plane can be found then there is collision. Note that the complexity for this test for n objects is O n2. We compared our proposed algorithm against this algorithm for environments containing differing num- bers of the same sphere objects triangular patches.

In particular, we tested both algorithms in environments with 10, 20, 30, and 40 moving sphere objects; at the last cycle of the tests two of the sphere objects collided. For 10 sphere objects, our algorithm performed roughly the same as the separating plane algorithm; in particular, our algorithm required 16 milliseconds of computation at the last cycle, while the separating plane algorithm required approximately 10 milliseconds per cycle.

How- ever, for 20, 30, and 40 objects our algorithm per- formed better. In particular, for 20, 30, and 40 objects, our algorithm required 21, 22, and 41 milliseconds at the last cycle; against this, the separating plane algorithm required approximately 35, 76, and milliseconds per cycle.

The computation times were measured by a Silicon Graphics Indigo2. Computation time for each processing cycle for the algorithm proposed in this paper, and is representative of proposed algorithm solid lines and the separating plane algorithm the bounding region hierarchy, octree, and voxel ap- dotted lines for 10, 20, 30, and 40 identical sphere objects proaches described in Section 2.

Essentially, the modifi- triangular patches each. Then, face octrees that intersect with the overlap regions. Computation time for each processing cycle for the proposed algorithm and the octree update algorithm for the environment of Figure Figure The experimental environment used to obtain the data for Figure The experiment that was performed the node checklist and the standard octree nodes.

Fi- was to move the Venus head and the space shuttle to- nally, for each standard octree voxel found to contain ward each other with translation and rotation until transformed black nodes from more than one object, all they collided at the last cycle; the other two objects also unique pairs of faces, where the faces are inside a pre- translated and rotated slightly without any collision. Basically, the octree update algo- the last cycle the octree update algorithm required rithm substitutes precomputed face octree black nodes milliseconds of computation, while the proposed algo- for faces in checking for intersection with overlap re- rithm required only 11 milliseconds roughly 16 times gions and standard octree nodes.

Note that this algo- better performance. Figure 14 shows the results of an experiment in which The third algorithm is a distance-based approach we tested the proposed algorithm against this octree up- Cohen, et al. Sections on vector and matrix algebra provide the background for advanced topics such as Voronoi regions, Minkowski sums, and linear and quadratic programming. Of utmost importance to programmers but rarely discussed in this much detail in other books are the chapters covering numerical and geometric robustness, both essential topics for collision detection systems.

Also unique are the chapters discussing how graphics hardware can assist in collision detection computations and on advanced optimization for modern computer architectures. The heart of any system that simulates the physical interaction between objects is collision detection-the ability to detect when two objects have come into contact.

This system is also one of the most difficult aspects of a physical simulation to implement correctly, and invariably it is the main consumer of CPU cycles. Practitioners, new to the field or otherwise, quickly discover that the attempt to build a fast, accurate, and robust collision detection system takes them down a long path fraught with perils and pitfalls unlike most they have ever encountered.

Without in-depth knowledge and understanding of the issues associated with engineering a collision detection system, the end of that path is an abyss that has swallowed many a good programmer!

Gino van den Bergen's new book is the story of his successful journey down that path. Along the way, he covers the topics of vector algebra and geometry, the various geometric primitives of interest in a collision system, the powerful method of separating axes for the purposes of intersection testing, and the equally powerful Gilbert-Johnson-Keerthi GJK algorithm for computing the distance between convex objects.

But this book provides much more than a good compendium of the ideas that go into building a collision system. The curse of practical computational geometry is floating-point arithmetic. Algorithms with straightforward implementations when using exact arithmetic can have catastrophic failures in a floating-point system.

Specifically, intersection and distance algorithms implemented in a floating-point system tend to fail exactly in the most important case in a collision system-when two objects are just touching. Great care must be taken to properly handle floating-point round off errors.

Gino's ultimate accomplishment in this book is his presentation on how to correctly implement the GJK distance algorithm in the presence of single-precision floating-point arithmetic. And what better way to illustrate this than with a case study, the final chapter on the design and implementation of SOLID. Gino implemented collision detection and physics in NaN Technologies' Blender, a creation suite for interactive 3D content.

Computer graphics is now used in various fields; for industrial, educational, medical and entertainment purposes. The aim of computer graphics is to visualize real objects and imaginary or other abstract items. In order to visualize various things, many technologies are necessary and they are mainly divided into two types in computer graphics: modeling and rendering technologies. This book covers the most advanced technologies for both types.

It also includes some visualization techniques and applications for motion blur, virtual agents and historical textiles. This book provides useful insights for researchers in computer graphics. Open world games have tremendously become a demanding criterion for computer games development as user be able to freely roam through land and sea virtually. One of the elements involving computer games development is to bring applicable real-time collision detection for each object.

Expand the voxel space so that the value of a voxel is the integral value of the distance of that voxel from the closest obstacle voxel.

Otherwise, D is not in collision with any obstacles in O. Let D be a spherical approximation of a servo-controlled device, which can be positioned within a space shared by a set of obstacles O.

Let P be the next position of the device D. A method which will ensure the collision free motion of D within the space is:. Read next position P from the servo-controller. Detect the collision status of D with O if in position P. Otherwise, do not move D to P. Repeat steps 2 and 3. Note that the next desired position of the device D must be close enough to the current position of the device D so that the change in voxel occupancy of any sphere in D does not exceed one voxel.

Let P be the next position of the device D as input from the servo-controller. If the configuration of D is under constrained by the position P, then there will exist a range of configurations of D which will satisfy P. For a set of configurations of D which position the device at P, detect the collision status of D with O. Order the configurations within the set by the closeness of collision with O.

If the configuration of D which is furthest from collision is collision-free, then move D to P in this configuration. The above representations provide the framework for a straightforward collision detection method.

The forward kinematic solution is applied to each link of the spherical manipulator model, and the center of each sphere is compared to the voxel corresponding to its location. If the value of the voxel is not greater than the radius of the sphere, then the manipulator in its modeled position is deemed to be in collision with some obstacle.

Advantageously, this time performance is independent of the number of obstacles in environment. A tradeoff which has been made to achieve this high performance is resolution. The resulting path can be planned only within a certain clearance of the obstacles in the environment, equal to the voxel size i. However, this restriction is reasonable for gross motion planning. What we claim is: 1.

In a device having one or more moveable elements residing within a finite space, a method of detecting a collision state between an object within the finite space and a model of the one or more moveable elements, comprising the steps of: a determining relative strengths of a set of discrete points throughout the space, the relative strength of any point being a measure of the distance from that point to the object;.

The method defined in claim 1 further comprising the step of redirecting the moveable element if a collision state is detected. The method as defined in claim 1 further comprising the step of: g repeating steps e to f for incrementally different positions of the model of the one or more moveable elements positioned at different locations within the finite space to determine a plurality of collision free states until a collision state is detected.

The method defined in claim 1 wherein each discrete point comprises a voxel. In a device having at least one relatively moveable element, a method of detecting a collision state between an object and a model of the device comprising the steps of: a determining the value of the strength of each of a plurality of voxels within a finite space, the strength of any voxel being an indicator of the distance from that voxel to the object;.

The method according to claim 5 further comprising the step of preventing the at least one moveable element from moving closer to the object when the ratio of the value of the strength of the voxel at the center of the sphere divided by the number of adjacent voxels that correspond to the radius of the sphere is less than one.

The method as defined in claim 5 further comprising the step of: d repeating steps b and c for incrementally different positions of the model of the one or more moveable elements to determine a plurality of collision free states, until a collision state is detected. The method according to claim 5 wherein the step of determining the value of the strength of each of a plurality of voxels within the finite space comprises the steps of: assigning all voxels located a distance from the object a value which corresponds to the distance in units of voxels from the object, wherein a first set of voxels occupying a space next to the object are assigned a value of one, and a second set of voxels occupying a space adjacent the first set of voxels and being a distance one voxel away from the object are assigned a value of two, and so on, such that a set of voxels that are located a distance less than the width of n voxels and greater than or equal to the width of n-1 voxels from the object are assigned a value of n.

The method according to claim 5 wherein the volume approximated by the one or more spheres corresponds in location to a layer extending along the surface of the moveable element, the thickness of the layer being equal or less than the diameter of the one or more spheres. USA en. CAC en. Method of automatic collision prevention for manipulator in working area bounded by obstructions. Navagation with optimum viewpoints in three-dimensional workspace interactive displays having three-dimensional objects with collision barriers.

USB1 en. Interference checking apparatus and method for checking interference of objects in computer. Image processing system to control vehicle headlamps or other vehicle equipment. Method and apparatus for limiting the movement of a robot, and a robot equipped with said apparatus. Movement monitoring method for monitoring the movement of a handling element, e.

Robot with a control unit for controlling a movement between an initial pose and an end pose. A method and a device for avoiding collisions between an industrial robot and an object.

Method for preventing and device for controlling colliding between cooperated manipulators. Control method for synchronous high speed motion stop for multi-top loaders across controllers. Method for controlling the movement of a mobile part of an x-ray recording system, and an x-ray recording system coupled to video cameras.

EPA1 en. Method and device for computer-aided testing of the constructability of a product. Interference inspection of multi-arm robot system by three-dimensional automatic region. USB2 en. DEA1 en. Method for preventing deadlock of a pair of robots in multi-robot system, involves avoiding deadlock condition during execution of programs by automatically determining and executing deadlock-free motion statement.

Device for determining interference of industrial machine, method for determining interference, computer program and recording medium. Real time explosive hazard information sensing, processing, and communication for autonomous operation. System and method for controlling exterior vehicle lights responsive to detection of a semi-truck. System and method for controlling vehicle equipment responsive to a multi-stage village detection. Vehicle imaging system and method for distinguishing reflective objects from lights of another vehicle.

Path planning and collision avoidance for movement of instruments in a radiation therapy environment. Imaging system including dynamic compensation for color attenuation for vehicle windscreens. USDS1 en. Vehicle imaging system and method for distinguishing between vehicle tail lights and flashing red stop lights. DEB4 en. Method of determining interference, determining interference system and storage medium.

Calculation method of closest point between relatively-moving substances and interference evaluation method. System and method for detection and avoidance of collisions of robotically-controlled medical devices. The safety predicting method in advance of both arms service robot operation under a kind of dynamic environment. System and method for processing streamed video images to correct for flicker of amplitude-modulated lights.

Interference determination method, interference determination system, and storage medium. A kind of Multi-axis Machining interference detection and processing method based on two-stage voxelization model. Method for preventing collision of two mutually movable bodies and an apparatus including an arrangement for preventing collision. Method of converting continuous three-dimensional geometrical representations into discrete three-dimensional voxel-based representations within a three-dimensional voxel-based system.

Method and apparatus for anti-collision and collision protection for multiple robot system.