KR101048018B1 - Real-Time Collision Detection Method and System Using Conservative Forward Technique - Google Patents

Abstract

Disclosed are a real-time collision detection method and system using a conservative forward technique. Real-time collision detection method using a conservative forward technique according to the present invention comprises the steps of (a) forming a boundary volume hierarchy for the two models to be examined for collision; (b) traversing the formed boundary volume hierarchy while performing a nearest distance query, calculating a time step for the conservative advance technique for some of the resulting boundary volume pairs, and finding the minimum time step among them; ; (c) advancing at least one of the two models according to the obtained minimum time step and repeating step (b); And (d) calculating the collision times of the two models by summing the time steps obtained through the repeated step (b). According to the present invention, it is possible to perform continuous collision checking in real time, and the processing speed is faster and the continuous collision checking speed for the polygon soup model can be improved.

Collision detection, continuous collision detection, conservative advancement

Description

Method and system for real-time collision detection using conservative advance technique {Method and system for continuous collision detection using conservative advancement}

The present invention relates to a real-time collision detection method and system, and more particularly, to a real-time collision detection method and system using a conservative forward technique.

Collision and distance queries are important issues in robotics, computer graphics, and geometric modeling. In particular, reliable and fast collision checking algorithms are required for dynamic simulations that require robot motion planning and non-penetration constraints. Collision checking problems have been extensively studied by many researchers in the field. Most of the early approaches to collision checking focused on static scenes in which the queried objects were placed statically in space. In recent years, researchers have focused on dynamic scenes in which objects can move, and in some dynamic scenarios, the entire motion trajectory of an object can be known as a function of time. The motion of an object is not known a priori, only a few sampled positions are known, for example in sampling-based robot motion planning, sampling the robot's collision-free configurations, and then successively colliding them from initial to final configuration. Used to calculate missing paths.

At a broad level, dynamic collision detection algorithms can be divided into two categories: discontinuous and continuous. Discrete algorithms use a static collision checking algorithm to check for collisions only in the sampled configurations. As a result, the static collision checking algorithm may miss a collision between two subsequent configurations. This is also known as the tunneling problem. On the other hand, Continuous Collision Detection (CCD) algorithms, first of all, perform tunneling problems by performing continuous motion interpolation between subsequent configurations and checking for collisions using interpolated motion. I can solve it. Thus, the CCD does not miss any possible collisions between the configurations. However, the main weakness of CCD algorithms is that they are generally slower than discrete algorithms. And most of the previous studies in the continuous collision test are limited to a polyhedral model or an articulated model, which consider connectivity information or topology information. This approach is intractable on a generic model represented by a polygon-soup model, such as a triangle-soup model without connectivity information.

The technical problem to be achieved by the present invention is to perform a continuous collision check in real time, real-time collision detection method and system using a conservative forward technique, which is fast processing speed and applicable to polygon soup model, and a program for executing the method A computer readable recording medium having recorded thereon is provided.

In order to solve the above technical problem, a real-time collision detection method using a conservative forward technique according to an aspect of the present invention, (a) forming a boundary volume hierarchy for the two models to examine the collision; (b) traversing the formed boundary volume hierarchy while performing a nearest distance query, calculating a time step for the conservative advance technique for some of the resulting boundary volume pairs, and finding the minimum time step among them; ; (c) advancing at least one of the two models according to the obtained minimum time step and repeating step (b); And (d) calculating the collision times of the two models by summing the time steps obtained through the repeated step (b).

In order to solve the above technical problem, a real-time collision detection system using a conservative forward technique according to an aspect of the present invention, the boundary volume layer structure forming unit for forming a boundary volume hierarchy for the two models to examine the collision; While traversing the boundary volume hierarchy formed while performing the nearest distance query, the time step for the conservative advance technique is calculated and the minimum time step among them is calculated for some boundary volume pairs obtained. A time step calculator which repeats this with the advanced model; A model advancement unit for advancing at least one of the two models by the obtained minimum time step; And a collision time calculator that calculates the collision time of the two models by summing the time steps obtained through the time step calculator.

In order to solve the above technical problem, a real-time collision inspection method using a conservative forward technique according to another aspect of the present invention, while repeating the process of obtaining a time step for conservative forward while performing the nearest distance query, As an input for the obtaining process, receiving the two nodes of the boundary volume hierarchy of the two models, the previously obtained current nearest distance, and the previously obtained current time step, and obtaining the time step may include (a) the two nodes. Is a leaf node, obtains the distance of the boundary volume pair, compares the calculated distance with the current nearest distance, updates the current nearest distance according to the result, and obtains a time step for conservative advancement of the boundary volume pair. Calculate and compare the calculated time step with the current time step and accordingly Updating the current time step; And (b) if at least one of the two nodes is not a leaf node, obtain a distance of a boundary volume pair corresponding to a child node and another node of the at least one node, and compare the obtained distance with the current nearest distance, According to the result, optionally, the child node and the other node are inputted to recursively obtain the time step or to conservatively advance the boundary volume pairs corresponding to the child node and the other node. Calculating a time step.

In addition, the present invention provides a computer-readable recording medium having recorded thereon a program for executing a real-time collision detection method using a conservative forward technique according to the present invention.

According to the present invention described above, the continuous collision check can be performed in real time, the processing speed is faster and the continuous collision check speed for the polygon soup model can be improved.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following description and the accompanying drawings, substantially the same components are denoted by the same reference numerals, and redundant description will be omitted. In addition, in the following description of the present invention, if it is determined that a detailed description of a related known function or configuration may unnecessarily obscure the subject matter of the present invention, the detailed description thereof will be omitted.

와

를 3D 내의 두 폴리곤-수프 모델을 감싸는 컨벡스 경계 볼륨이라고 하고, 여기서

는 강체 변환(rigid transformation) M(t) 하에서 움직일 수 있고,

는 고정되어 있다고 하자.

가 고정되어 있다고 하더라도 일반성을 잃지 않는다. 그리고

의 초기와 마지막 컨피규레이션이 시간 t=0 와 시간 t=1에서 각각

와

으로 주어진다고 가정하고,

=M(t)

라 정의한다. 그러면 연속적 충돌 검사의 문제는 다음 수학식 1이 비공백(non-empty)인지 검사하는 것으로 공식화될 수 있다.First, a conservative advancement technique employed in an embodiment of the present invention will be described. 1 is a reference diagram for explaining a conservative forward technique, taking a line swept sphere as an example.

Wow

Is called the convex boundary volume that encloses two polygon-soup models in 3D, where

Can move under rigid transformation M (t),

Is fixed.

Even if is fixed, it does not lose its generality. And

The initial and last configuration of are at time t = 0 and time t = 1 respectively

Wow

Assume that given by

= M (t)

It is defined as The problem of continuous collision checking can then be formulated as checking that Equation 1 is non-empty.

Furthermore, if Equation 1 is non-blank, calculate the initial time of contact (TOC) τ, which is the minimum value of t that satisfies the transplant.

를 Δt_i 만큼

를 향하여 전진시킴으로써 τ 의 하계(lower bound)를 계산하는 단순한 테크닉이다. 도 1을 참조하면, Δt_i 는

와

사이의 가장 가까운 거리

에 대한 하계와 단위 시간당

로 사영되는

의 모션의 상계(upper bound) μ 에 기초하여 계산된다. 즉, 다음 수학식과 같다.Conservative forward techniques repeatedly iterate while avoiding collisions between two convex objects.

By Δt _i

It is a simple technique to calculate the lower bound of τ by advancing toward. Referring to Figure 1, Δt _i is

Wow

The closest distance between

Summer and unit per hour for

Projected with

Calculated based on the upper bound μ of the motion of. That is, it is as follows.

와

간의 최소 거리인

가 어떤 사용자 지정된 거리 임계값보다 작을 때까지, 전진 시간 스텝(advancement time-step)을 반복하고 그것을 합계함으로써(즉,

) 구해진다.Then the initial contact time is

Wow

Is the minimum distance between

By repeating the advance time-step and summing it up (i. E., Until <

)

의 초기 및 최종 컨피규레이션만이

와

으로 주어지는 것으로 가정한다. 이 컨피규레이션들을 이용하여

와

을 보간하기 위하여, 일정한 병진 속도(translational velocity)와 회전 속도(rotational velocity)를 가지는 연속 모션 M(t)를 생성한다. 이에 관하여는 문 헌 [X. Zhang, M. Lee, and Y. J. Kim, "Interactive continuous collision detection for non-convex polyhedra," The Visual Computer, pp. 749??760, 2006.]에 자세히 설명되어 있다.2 is a flowchart of a real-time collision detection method using a conservative forward technique according to an embodiment of the present invention. In this embodiment,

Only the initial and final configuration of the

Wow

Assume that given by Using these configurations

Wow

In order to interpolate, a continuous motion M (t) having a constant translational velocity and a rotational velocity is generated. In this regard, Moon Hun [X. Zhang, M. Lee, and YJ Kim, "Interactive continuous collision detection for non-convex polyhedra," The Visual Computer, pp. 749 ?? 760, 2006.].

Referring to FIG. 2, in step 210 as a preprocess, a bounding volume hierarchy (BVH) is formed for two models for which collision is to be checked. In one embodiment, a swept sphere volume (SSV) hierarchy is used. SSV is a boundary volume consisting of one of the so-called point swept sphere (PSS), line swept sphere (LSS) and rectangle swept sphere (RSS). SSV hierarchy is formed recursively using SSV as a node. 3 shows a simple example of the boundary volume hierarchy formed for the two models. Formation of SSV hierarchies, distance and proximity calculations using them are described in E. Larsen, S. Gottschalk, M. Lin, and D. Manocha, "" Fast proximity queries with swept sphere volumes, "" Department of Computer Science, University of North Carolina, Tech. Rep. TR99-018, 1999.].

In step 220, the BVH is traversed while performing close distance queries with the BVH, and the time step for the conservative forward technique is calculated for some boundary volume pairs. Find the minimum time step among them.

In this step, the calculation of the time step of conservative advance is optionally applied to the nodes in the BVH. As can be seen from Equation 2, the conservative forward technique requires two components, the closest distance and the motion bound. Therefore, it is necessary to calculate the closest distance and motion bound between SSVs. The closest distance between SSVs is obtained as a byproduct during close distance query performance, but the tight upper bound μ of motion for SSV should be calculated. This will be described later.

In addition, an important calculation in this step is to determine which nodes in the hierarchy will be candidates for the calculation of the time step of conservative advancement. One choice is to have nodes that stop traversing the BVH during the nearest query, which are called front nodes. This is because these nodes have a higher probability of realizing τ than other nodes. However, the depth of the front nodes in the hierarchy is relatively deep and therefore the number of front nodes is also large. The depth or number of front nodes affects the performance of the algorithm because successive collision checks require the application of conservative forward techniques repeatedly to these nodes. Thus, in one embodiment, a technique for improving performance by adjusting the depth of front nodes during an iteration of conservative advance is presented. This will also be described later.

Referring to FIG. 2, when a minimum time step is obtained in step 220, in step 230, one of the two models (or two models respectively) is advanced by the minimum time step. In step 240, the closest distance between the two models (this distance is obtained through the closest distance query in step 220) is less than a predetermined predetermined threshold value, and if not, the control returns to step 220 with the advanced model. Perform step 220.

After repeating steps 220 to 240 a plurality of times, if it is determined in step 240 that the distance between the two models is smaller than the predetermined threshold value, the process proceeds to step 250 and the two models collide by summing the time steps obtained through the repeated 220 steps. Find the time (TOC).

Hereinafter, a process of calculating the upper limit μ of the motion with respect to the SSV according to an embodiment of the present invention will be described. Here, we present a method for obtaining the motion bound μ for boundary volumes and triangular primitives. These primitives are assumed to follow the rigid body transformation M (t) with a constant translation speed v and rotational speed ω.

를 구성하는 경계볼륨 또는 삼각형 프리미티브라 하고 β를

를 구성하는 경계볼륨 또는 삼각형 프리미티브라 하자. 나아가,

를 α 상의 점이라 하고,

을 α, β 사이의 가장 가까운 방향이라 하고,

를

가 속한 로컬 바디 프레임의(local body frmae)의 원점으로부터

로의 벡터라 하자. 그러면

위로 사영되는 α 의 최대 궤도 길이(또는 모션 바운드)는 다음 수학식과 같다.First, a method of obtaining the motion bound μ for the boundary volume will be described. In this embodiment, the selection of the boundary volume is SSV. SSV is composed of PSS, LSS, and RSS, which are defined as Minkowski sums of spheres, points, lines, and rectangles in 3D, respectively. . 4 is a diagram illustrating a PSS, an LSS, and an RSS. to calculate the motion bound of α

Is the boundary volume or triangle primitive that

Let it be the boundary volume or triangle primitive constituting. Furthermore,

Is a point on α,

Is the closest direction between α and β,

To

From the origin of the local body frame it belongs to

Let's call it a vector. then

The maximum orbital length (or motion bound) of α projected up is given by the following equation.

이고,

은 M(t)의 회전 성분이다. 상기 수학식 3에서, 첫 번째 항은 상수이므로, 두 번째 항을 최대화여야 한다. 여기서,

는 동일 평면 상에 있고(coplanar), 노멀(normal)이 ω 인 평면 S를 형성하게 된다. 상기 수학식 3에서 두 번째 항의 극대치는 아래 수학식에 보여지는 바와 같이 평면 S 상으로의

의 최대 투사(maximal projection)에 의해 얻어질 수 있다. 즉, α 를 SSV라 하면, α 의 모션 바운드 μ 는 다음 수학식과 같다.here,

ego,

Is the rotational component of M (t). In Equation 3, since the first term is a constant, the second term should be maximized. here,

Is coplanar and forms a plane S with normal ω. The maximal value of the second term in Equation (3) above the plane S phase as shown in the following equation.

It can be obtained by maximal projection of. That is, if α is SSV, the motion bound μ of α is expressed by the following equation.

이고, r 은 SSV를 형성하기 위해 사용되는 구의 반지름이며,

는 SSV의 생성 프리미티브(PSS, LSS 및 RSS의 생성 프리미티브는 각각 점, 직선, 직사각형이다)의 끝점(endpoint)이다. here,

R is the radius of the sphere used to form the SSV,

Is the endpoint of the SSV generation primitives (PSS, LSS and RSS generation primitives are points, straight lines, and rectangles, respectively).

라 할 수 있다. 여기서

는

의 바디 프레임의 원점으로부터 SSV의 생성 프리미티브 상의 한 점으로의 벡 터이다. 그러면 다음 수학식을 얻을 수 있다.Furthermore, for all three types of SSV

It can be said. here

Is

Is the vector from the origin of the body frame to a point on the generation primitive of the SSV. Then we can get

는

의 평면 S 로의 사영이다. here,

Is

Projection to plane S of.

의 평면 S 로의 사영은 SSV의 생성 프리미티브의 평면 S로의 사영 내에 존재하여야 하고, 다음 수학식을 얻을 수 있다.According to the projection geometric theory, the projection of a point into a plane is a point, the projection of a straight line into a plane is a straight line or a point, and the projection of a rectangular plane into a plane is a rectangle or a straight line. therefore

The projection into plane S of must be within the projection of the generation primitive of SSV into plane S, and the following equation can be obtained.

Equation 4 is proved by Equations 3, 5, and 6 described above.

We now describe how to find the motion bound μ for a triangular primitive. The motion bound of the triangle primitive can be obtained by projecting the vertices of the triangle to the boundaries of the projection range. That is, if α is a triangular primitive, the motion bound μ of α is expressed by the following equation.

이며,

는 α 의 정점들이다. 증명은 상기 수학식 4와 유사하므로 생략한다.here,

Is,

Are the vertices of α. The proof is similar to Equation 4, and is omitted.

Now, in one embodiment of the present invention, a technique for improving performance by adjusting the depth of front nodes during an iteration of conservative advance is described. The basic idea is that for the first few iterations of conservative advance it is not necessary to accurately calculate the closest distance. Only the correct distance is needed for the final iteration of conservative advancement. The choice of distance approximation will determine the depth of the front nodes or their number.

Prior to the description of this embodiment, the cost function for performing the real-time collision check will be analyzed. A simple formula for measuring the performance of the real-time collision check can be expressed as the following equation.

Where T is the overall cost function for the real-time collision check, T _BVH is the cost to form BVH for each model, N _τ is the total number of conservative forward iterations to find τ, and N _BV is the conservative forward Is the number of boundary volume pairs applied, i.e., calculates the time step, and T _CA is the cost for calculating the conservative forward equation according to Equation 2 above. In general, since T _BVH and T _CA are constants during run time, it is necessary to reduce N _τ and N _BV to improve performance.

As already explained, this embodiment applies a conservative forward technique to the front nodes found during the nearest distance query. Therefore, N _BV corresponds to the number of these front nodes. In order to reduce N _BV , it is necessary to reduce or adjust the depth of the front nodes, in this embodiment by doing so by terminating the traverse of BVH early during the nearest distance query.

가 원래 나올 값보다 더 작기 때문에 상기 수학식 2에 기초한 전진 시간 스텝 Δt_i 는 역시 덜 엄격할 것이다. FIG. 5 is a diagram of front nodes with different depth values, showing that different front nodes are obtained by terminating recursion early during the nearest distance query with approximate and accurate distance values. Referring to FIG. 5, the result of the early termination generally yields only approximate distances smaller than the actual nearest distance. therefore

The advancing time step Δt _i based on Equation 2 above would also be less stringent because is smaller than the original value.

Reducing N _BV for just a few iterations may eventually require more conservative forward iterations. Therefore, it may be nearly impossible to reduce both N _τ and N _BV simultaneously. Therefore, it is necessary to balance N _τ and N _BV to minimize the cost function. As an example, to prevent the number of repetitions of excessive conservative advances, it is checked for each iteration that the approximate distance is less than which threshold or the number of repetitions N _{τ to date} is too large. If so, return to the normal nearest-range query method without early termination of the BVH traverse.

In one embodiment, as a method for performing early termination during a nearest distance query, during a recursive call for a distance query, a modified distance (hereinafter, modified current nearest distance) that is smaller than a previously obtained nearest distance. Is supplied to the recursive function by pretending to be the current nearest distance. This causes the recursive distance query to be terminated early when the recursion cannot improve the simulated current nearest distance value. Finally, after all recursions are completed, we collect the front nodes that have stopped recursion and perform conservative forward operations on them. That is, a time step for conservative advancement is calculated for boundary volume pairs corresponding to front nodes.

와

, 현재 최근접 거리

, 현재 전진 시간 스텝

, 그리고 재귀의 터미네이션을 조절하기 위한 변수 값

를 입력으로 한다. 출력으로는 업데이트된

및

가 출력되며, 출력된

및

는 다음 반복을 위한 입력이 된다. 처음 실행에서는 BVH의 루트 노드

와

, 현재 최근접 거리로서 ∞, 현재 전진 시간 스텝으로서 1, 그리고

(

)가 입력된다. 변수 값

는 사용자에 의해 미리 지정될 수 있다. FIG. 6 illustrates a pseudocode of a specific embodiment of step 220. The illustrated water code will be referred to as C ² A for convenience. The water code shown is an input, nodes of BVH

Wow

, Current nearest street

, Current forward time step

, And variable values to control recursion termination

As input. Updated as output

And

Is outputted, and

And

Is the input for the next iteration. In the first run, the root node of BVH

Wow

∞ as the current nearest distance, 1 as the current forward time step, and

(

) Is entered. Variable value

May be predefined by the user.

보다 크거나, 또는 앞선 반복에서 얻어진 현재 최근접 거리

가 소정 임계값

보다 작은지 검사하고, 그렇다면

=1로 리셋한다. 보수적 전진의 반복이 진행될수록 그 반복 회수는 늘어나고

는 작아진다. 따라서 보수적 전진의 초기 일부 반복에서는

가 1보다 작도록 설정되고, 그 후에 보수적 전진 반복의 마지막을 향하여는

가 1로 리셋된다.

가 1보다 작도록 설정되면 후술할 알고리즘 내에서 이른 터미네이션이 일어나고,

가 1로 설정되면 후술할 알고리즘 내에서 보통의 최근접 거리 질의가 수행된다.Referring to Fig. 6, first, in lines 1 to 3, the number of repetitions of conservative advance, that is, the number of repetitions of 220 steps is a predetermined threshold value.

The current nearest distance greater than or obtained from a previous iteration

Is a predetermined threshold

Is less than

Reset to = 1. As the iteration of conservative advances progresses, the number of iterations increases

Becomes smaller. So in some early iterations of conservative advance,

Is set to be less than 1, and then towards the end of the conservative forward iteration

Is reset to 1.

If is set to less than 1, early termination occurs within the algorithm to be described later,

If is set to 1, a normal nearest distance query is performed in the algorithm to be described later.

Next, the lines 4 to 10 will be described.

와

가 만일 리프 노드(leaf node)라면

와

사이의 거리 d 를 계산한다. 이때 PQP(Proximity Query Package) 라이브러리를 사용할 수 있다. 그리고 d가

보다 작다면

를 d로 업데이트한다. 그리고 수학식 2를 사용하여 d,

와

를 가지고

를 구한(라인 7) 다음,

가

보다 작다면

를

로 업데이트한다. 라인 7이 수행될 때

와

는 프론트 노드가 된다. 마지막으로

와

값을 리턴한다.Node

Wow

Is a leaf node

Wow

Calculate the distance d between In this case, PQP (Proximity Query Package) library can be used. And d

If less than

Update to d. And using equation 2, d,

Wow

Have

After obtaining (line 7),

end

If less than

To

Update to. When line 7 is performed

Wow

Becomes the front node. Finally

Wow

Returns a value.

Next, the lines 11 to 19 will be described.

가 리프 노드가 아니라면(라인 11),

의 왼쪽 자식 노드를 A로 하고,

의 오른쪽 자식 노드를 B로 하고,

를 C와 D로 한 다음, A와 C의 거리 d₁(즉,

의 왼쪽 자식 노드에 해당하는 경계볼륨과

간의 거리)과 B와 D와의 거리 d₂(즉,

의 오른쪽 자식 노드에 해당하는 경계볼륨과

간의 거리)를 계산한다. 만일

가 리프 노드라면(라인 15),

가 리프 노드가 아닐 것이므로,

를 A와 B로 하고,

의 왼쪽 자식 노드를 C로 하고

의 오른쪽 자식 노드를 D로 한 다음, A와 C의 거리 d₁과 B와 D와의 거리 d₂를 계산한다. if

Is not a leaf node (line 11),

Let A be the left child node of,

Let B be the right child of,

With C and D, then the distance between A and C d ₁ (i.e.

The bounding volume corresponding to the left child node of

Distance) and the distance between B and D d ₂ (i.e.

The boundary volume corresponding to the right child node of

Distance). if

If is a leaf node (line 15),

Is not a leaf node, so

With A and B,

Let the left child node of C be

One of the right child node, and D, and then calculates the distance d ₁ and distance d ₂ between B and D in the A and C.

Next, the lines 20 to 46 will be described.

와 비교하여 그 결과에 따라 C²A의 재귀호출을 하던지 보수전 전진을 위한 시간 스텝을 계산한 후, 다음으로 d₂와 d₁ 중 큰 값을 가지고 마찬가지로

와 비교하여 그 결과에 따라 C²A의 재귀호출을 하던지 보수전 전진을 위한 시간 스텝을 계산한다. 여기서,

가 (

일 때) 상기된 수정 현재 최근접 거리가 된다.If d ₂ is smaller than d ₁ , lines 21 to 32 to be described below are performed, otherwise, that is, if d ₂ is not smaller than d ₁ , lines 34 to 45 to be described below are performed. That is, referring to FIG. 5, first of all, a smaller value of d ₂ and d ₁ is obtained.

As compared to then calculate the time for the former step Either a recursive call of the C ² A repair advanced with the result, and then to similarly have a larger value of d ₂ and d ₁

Compute the time step for recursive or precompensation advancement of C ² A according to the result. here,

(

Is the current closest distance.

The lines 21 to 32 performed when d ₂ is smaller than d ₁ will be described.

보다 작은지 검사하고(라인 21), 그렇다면 C²A(B, D,

,

,

)를 리턴하는 재귀를 수행한다. 즉, B와 D, 앞서 얻어진 현재 최근접 거리

, 앞서 얻어진 현재 시간 스텝

, 그리고

를 입력으로 하여 C²A를 수행하고 업데이트된 출력값

및

을 리턴한다(라인 22). d₂가

보다 작은지 검사했는데, 그렇지 않다면 d₂와 B, D를 가지고 시간 스텝

를 계산(라인 24)한 후,

가 앞서 얻어진 현재 시간 스텝

보다 작다면

를

로 업데이트한다(라인 25). 여기서, d₂와

를 비교하게 되는데, 만일

가 1보다 작은 값이라면(즉, 이른 터미네이션)

가 1인 경우보다 라인 24가 일찍 수행되므로 재귀호출의 이른 터미네이션, 즉 계층구조 트래버스의 이른 터미네이션이 일어나게 된다. 라인 24가 수행될 때 B와 D가 프론트 노드가 된다.

가 1이라면, 이른 터미네이션을 하지 않고 보통의 최근접 거리 질의가 된다. d ₂

Is less than (line 21), then C ² A (B, D,

,

,

Perform a recursion that returns). Ie B and D, the current nearest nearest distance

, The current time step obtained earlier

, And

C ² A using as input and updated output

And

Returns (line 22). d ₂

If not, check the time step with d ₂ and B, D

After calculating (line 24),

Time step obtained earlier

If less than

To

(Line 25). Where d ₂ and

Is compared to

Is less than 1 (ie, early termination)

Since line 24 is performed earlier than 1, early termination of the recursive call, that is, early termination of the hierarchical traverse, occurs. When line 24 is performed, B and D become front nodes.

If 1, then the normal nearest distance query is made without early termination.

보다 작은지 검사하고(라인 27), 그렇다면 C²A(A, C,

,

,

)를 리턴하는 재귀를 수행하고(라인 28), 그렇지 않다면 d₁과 A, C를 가지고 시간 스텝

를 계산(라인 30)한 후,

가 앞서 얻어진 현재 시간 스텝

보다 작다면

를

로 업데이트한다(라인 31). 라인 27 내지 32의 취지는 라인 21 내지 26의 취지와 동일하다.Now d ₁

Is less than (line 27), and if so C ² A (A, C,

,

,

Perform a recursion returning () (line 28), otherwise time step with d ₁ , A, and C

After calculating (line 30)

Time step obtained earlier

If less than

To

(Line 31). The purpose of lines 27 to 32 is the same as that of lines 21 to 26.

Lines 34 to 45 performed when d ₂ is not smaller than d ₁ are the same as the description of lines 21 to 32 described above, except that only the order of d ₁ and d ₂ is changed.

가 어떤 상계(upper bound) 값

보다 크다면 해당 노드와 그 자식 노드들을 전지(prune)하는 것이다. 이때 초기적으로

로 설정하고, k 번째 반복에서

로 설정할 수 있다. 왜냐하면

이라는 것은 [0,1] 동안에 그 노드 n 에 대하여 충돌이 없음을 의미하고, k번째 반복에서 구해진 시간 스텝이 1에서 (k-1) 번째 반복까지 더해진 시간 스텝

을 뺀 값보다 크다면 t=1 이 되더라도 충돌이 없을 것이기 때문이다. 따라서 그러한 노드와 그 자식 노드들은 더 이상 검사할 필요가 없다.In addition, in one embodiment, the following simple technique may be further employed to further improve collision detection performance. In the i th iteration of conservative advance, when visiting a node n corresponding to the boundary volume pair, the time step of that boundary volume pair

Is any upper bound value

If it is larger, it prunes the node and its children. At this time

, At the k th iteration

Can be set to because

Means that there is no collision for that node n during [0,1], the time step obtained from the k th iteration plus 1 to the (k-1) iteration

If it is larger than minus, there will be no collision even if t = 1. Therefore, such nodes and their children do not need to be examined anymore.

7 is a block diagram of a real-time collision detection system using a conservative forward technique in accordance with an embodiment of the present invention. The collision inspection system according to the present embodiment includes a boundary volume hierarchy forming unit 710, a time step calculator 720, a model advance unit 730, and a collision time calculator 740. Although not shown, the collision inspection system includes two input models for which collision is to be checked, a model advanced by the model advance unit 730, a boundary volume hierarchy, and a time step calculated by the time step calculator 720. The memory may further include a memory in which the back is stored.

The boundary volume hierarchy forming unit 710 receives two models for checking collision, and forms a boundary volume hierarchy therefor. Since the operation of the boundary volume layer structure forming unit 710 is the same as that described in operation 210 of FIG. 2, a detailed description thereof will be omitted.

및 구해진 현재 시간 스텝

가 시간 스텝 계산부(720)의 출력이 되며,

는 후술할 모델 전진부(730)와 충돌 시간 계산부(740)로 입력되고,

및

는 다음 반복을 위하여 시간 스텝 계산부(720)로 다시 입력된다. 시간 스텝 계산부(720)의 동작은 도 2의 220단계에 관련된 설명과 동일하므로 구체적인 설명은 생략한다.The time step calculation unit 720 traverses the boundary volume hierarchy while performing the nearest distance query for the two models, and calculates the time step for the conservative forward technique for some of the boundary volume pairs obtained therefrom, and the minimum of them. Find the time step of. Current nearest distance between two models obtained by nearest distance query

And the current time step obtained

Becomes the output of the time step calculator 720,

Is input to the model advance unit 730 and the collision time calculation unit 740 to be described later,

And

Is input back to the time step calculator 720 for the next iteration. Since the operation of the time step calculator 720 is the same as that described in operation 220 of FIG. 2, a detailed description thereof will be omitted.

만큼 두 모델 중 어느 한 모델(또는 두 모델을 각각)을 전진시킨다. 전진된 모델은 시간 스텝 계산부(720)로 입력되고, 시간 스텝 계산부(720)는 전진된 모델을 가지고 반복적으로 상기된 동작을 수행하여

및

를 구한다. The model advance unit 730 is a time step obtained by the time step calculator 720

Advance one of the two models (or two models each). The advanced model is input to the time step calculator 720, and the time step calculator 720 repeatedly performs the above-described operation with the advanced model.

And

.

The repetitive operation of the time step calculator 720 and the model forwarder 730 is performed until the closest distance between the two models is smaller than a predetermined user specified threshold. If the closest distance between the two models is determined to be smaller than the predetermined threshold value, the collision time calculator 740 sums the time steps obtained from the time step calculator 720 until then to obtain the collision time TOC of the two models. .

According to the above-described embodiment, it is possible to efficiently calculate the motion bound for the SSV and to accelerate the performance of the continuous collision check by adjusting the depth or number of front nodes. Therefore, we can dramatically improve the speed of continuous collision checking of polygonal soup models, and we can do this at real-time speed, as long as the model is tessellated, so that it is in the geometry or topology of the model. It enables continuous collision checking without constraints and can have faster performance than continuous collision detection methods specialized for conventional polyhedral models.

Meanwhile, the above-described embodiments of the present invention can be written as a program that can be executed in a computer, and can be implemented in a general-purpose digital computer that operates the program using a computer-readable recording medium. The computer-readable recording medium may be a magnetic storage medium (for example, a ROM, a floppy disk, a hard disk, etc.), an optical reading medium (for example, a CD-ROM, DVD, etc.) and a carrier wave (for example, the Internet). Storage medium).

So far I looked at the center of the preferred embodiment for the present invention. Those skilled in the art will appreciate that the present invention can be implemented in a modified form without departing from the essential features of the present invention. Therefore, the disclosed embodiments should be considered in an illustrative rather than a restrictive sense. The scope of the present invention is shown in the claims rather than the foregoing description, and all differences within the scope will be construed as being included in the present invention.

1 is a reference diagram for explaining a conservative forward technique.

2 is a flowchart of a real-time collision detection method using a conservative forward technique according to an embodiment of the present invention.

3 shows a simple example of the boundary volume hierarchy formed for the two models.

4 is a diagram illustrating a PSS, an LSS, and an RSS.

5 is a diagram illustrating front nodes having different depth values.

FIG. 6 illustrates a pseudocode of a specific embodiment of step 220.

7 is a block diagram of a real-time collision detection system using a conservative forward technique in accordance with an embodiment of the present invention.

Claims (24)

In the real-time collision detection method using a conservative forward technique, (a) forming a boundary volume hierarchy for the two models for which collision is to be examined; (b) traversing the formed boundary volume hierarchy while performing a nearest distance query, calculating a time step for the conservative advance technique for some of the resulting boundary volume pairs, and finding the minimum time step among them; ; (c) advancing at least one of the two models according to the obtained minimum time step and repeating step (b); And (d) calculating the collision time of the two models by summing the time steps obtained through the repeated step (b); In the step (b), the distance of the boundary volume pair obtained while performing the nearest distance query is compared with the current nearest distance obtained earlier, and the traverse of the boundary volume hierarchy is terminated according to the result. Calculate the time step of the pair, In step (b) of at least the initial partial repetition, the modified current nearest distance obtained by multiplying the distance of the corresponding boundary volume pair by the predetermined value between 0 and 1 and the current nearest nearest distance is compared according to the result. Terminating the traverse of the boundary volume hierarchy and calculating the time step of the boundary volume pair at that time, When the previously obtained current nearest distance is smaller than a predetermined threshold or the number of repetitions of step (b) is larger than a predetermined threshold, the distance of the corresponding boundary volume pair and the boundary without using the modified current nearest distance are determined. And comparing the current nearest distance obtained earlier and terminating the traverse of the boundary volume hierarchy according to the result and calculating the time step of the boundary volume pair at that time. delete delete delete The method of claim 1, And terminating the traverse of the boundary volume hierarchy when the distance of the boundary volume pair is smaller than the modified current nearest distance or the previously obtained current nearest distance. delete delete delete The method of claim 1, And if the calculated time step is greater than a predetermined value in step (b), the corresponding nodes and their child nodes in the boundary volume hierarchy are batteryd. The method of claim 1, And the predetermined value is set to 1 in the first execution of the step (b) and in the following iterations according to the following equation.

Where k represents the number of times of said repetition,

Is the minimum time step obtained at the i th iteration. The method of claim 1, And the boundary volume is a swept sphere volume. The method of claim 11, The time step for the conservative advance technique is calculated based on the summer bound for the closest distance between the boundary volume pairs and the motion bound that is the upper bound of the motion of the boundary volume as long as the closest distance is projected per unit time. Collision checking method. The method of claim 12, When the boundary volume α follows a rigid body transformation M (t) having a translational speed v and a rotational speed ω

Is a point on α,

Is the closest direction between α and the other boundary volume β

Recall from origin

A vector of raw, The motion bound is,

Above on the plane S to form

Collision checking method, characterized in that obtained by the maximum projection of. The method of claim 13, Wherein the motion bound is obtained according to the following equation.

here,

R is the radius of the sphere used to form the SSV,

Is the endpoint of the generation primitive of the SSV. The method of claim 1, The step (b) is repeated until the nearest distance between the two models obtained according to the nearest distance query is smaller than a predetermined threshold value. A computer-readable recording medium having recorded thereon a program for executing a real-time collision detection method using the conservative advance technique according to any one of claims 1, 5, 9, and 10 to 15. In a real-time collision detection system using a conservative forward technique, A boundary volume hierarchy forming unit for forming a boundary volume hierarchy for two models to be examined for collision; While traversing the boundary volume hierarchy formed while performing the nearest distance query, the time step for the conservative advance technique is calculated and the minimum time step among them is calculated for some boundary volume pairs obtained. A time step calculator which repeats this with a model advanced by A model advancement unit for advancing at least one of the two models by the obtained minimum time step; A collision time calculator configured to calculate collision times of the two models by summing time steps obtained through the time step calculator; The time step calculation unit compares the distance of the boundary volume pair obtained while performing the nearest distance query with the current nearest distance obtained earlier, and terminates the traverse of the boundary volume hierarchy according to the result, and then the boundary volume pair at that time. Compute the time step of, but at least in the initial partial iteration, compare the modified current nearest distance obtained by multiplying the distance of the corresponding boundary volume pair by a predetermined value from 0 to 1 to the previously obtained current nearest distance and Accordingly, when the traverse of the boundary volume hierarchy is terminated, the time step of the boundary volume pair is calculated, and the previously obtained nearest nearest distance is smaller than a predetermined threshold or the number of times of repeating is larger than a predetermined threshold. The distance of the corresponding boundary volume pair without using the modified current nearest distance Collision detection system, characterized in that for comparing the current closest distance the previously obtained, and the traverse of the terminal carbonate bounding volume hierarchy according to the result and calculate the time step of the bounding volumes of the pair of time. delete delete delete delete delete delete delete

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