[高分求算法]平面球体碰撞的算法，比如台球游戏中球之间的碰撞。

2003-10-09 09:09:06 1.1k 阅读 AI 写同款 · GEO 优化AI 选题数据监测一键分发 ›

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基于DE2-115红外解码实验基于DE2-115红外解码实验一、功能描述在同一个遥控电路中通常要使用实现不同的遥控功能或区分不同的机器类型，这样就要求信号按一定的编码传送，编码则会由编码芯片或电路完成。对应于编码芯片通常会有相配对的解码芯片或包含解码模块的应用芯片。在实际的产品设计或业余电子制作中，编码芯片并一定能完成我们要求的功能，这时我们就需要了解所使用的编码芯片到底是如何编码的。只有知道编码方式，我... 阅读详情

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切换为时间正序

halfdream 2003-11-07

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Skt32(荒城之月)贴出来的已经足够消化一段时间了.

我觉得主要是碰撞那一霎间处理麻烦.
至于碰撞前碰撞后运动状态处理很简单的.
中学物理学两条定律,
1,动量守恒,作一下球的速度矢量分解与相加,就很容易算出
2,能量守恒,可以理解化为弹性碰撞,否则自己加一个百分之几的系数:)

有一个简单推论,质量相等的球弹性正碰,两个球彼此交换速度.

其实可以进一步推广,两个球非正碰的时候,
将球的速度矢量分解,按两球的切向和法向分解..
这样,法向的速度还是满足上面推论.
切向的速度则不受影响(忽略摩擦)

如果要进一步考虑非完全弹性碰撞,可以自己估计一个百分比系数.两球交换速度的时候
给它打个折扣.

要计算摩擦的影响也容易
球1切向速度=(1-摩擦系数)*球2切向速度

许野平 2003-10-23

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参考：http://search.csdn.net/expert/topic/6/603/2002/7/7/855997.htm

wcb2001 2003-10-17

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有代码吗？可以发给我看看吗？sunever999@hotmail.com，先谢谢啦

skywind 2003-10-16

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我怎么说嘛，再说就是公式了，这里又不方便帖，再说就是代码了。

wcb2001 2003-10-16

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to skywind(今何再)
大侠，能不能详细说说呢？

Skt32 2003-10-11

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koules：

　由Linux移植的程序，经典作品。

开发工具：VC++6.0 和 Directx

　程序及源程序下载(174k)

http://creativesoft.home.shangdu.net/koules.zip

Skt32 2003-10-11

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/ 5 …………………………………………………………………………………………………
但是我们的方法是有缺陷的。我们忘记在我们的方程中加入时间。图1显示了时间的重要性，因而它不能省去。就算一个物体不在时间 t1 或 t2 抵触，它可以在时间t1 < t < t2穿过t边界哪儿。这是非常正确的，我们已经有大而连续的框架可操作。我们会发现必须还要一个好方法来处理差异。
But our method is flawed. We forgot to include the time in our equation. Figure 1 shows that time is just too important to leave out. Even if an object doesn’t collide at time t1 or t2, it may cross the boundary at time t where t1 < t < t2. This is especially true when we have large jumps between successive frames (such as when the user hit an afterburner or something like that). We'll have to find a good way to deal with discrepancy as well.

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我们应该将时间作为第4维也加入到所有的计算中去。这些使得计算变得很复杂，然而，我们只能舍弃它们。我们也可从原来的物体在时间 t1 和 t2 之间的占据，然后靠着墙测试结果(图 2 )。
We could treat time as a fourth dimension and do all of our calculations in 4D. These calculations can get very complex, however, so we’ll stay away from them. We could also create a solid out of the space that the original object occupies between time t1 and t2 and then test the resulting solid against the wall (Figure 2).

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一条简单的途径就是在 2 不同的时间在一个物体的地点附近创造凸壳。这条途径的效率很低并且毫无疑问它会降低你游戏的执行速度。如果不建立凸壳，我们可以在物体附近建立一个范围框。在我们熟悉几种技术后，我们要再次回到这个问题上。
An easy approach is to create a convex hull around an object’s location at two different times. This approach is very inefficient and will definitely slow down your game. Instead of constructing a convex hull, we could construct a bounding box around the solid. We’ll come back to this problem once we get accustomed to several other techniques.

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另外的途径，它是更容易的实现但是少些精确,是在正中央为交叉的一半和测试细分给的时间间隔。
另外的途径,其是更容易的实现但是少些精确，是细分在为在midpoint 的交叉的一半和测试的给的时间间隔。这计算能递归地为每个结果的一半返回。这途径将比先前的方法更快，但是它不能保证精确检测所有碰撞的。
Another approach, which is easier to implement but less accurate, is to subdivide the given time interval in half and test for intersection at the midpoint. This calculation can be done recursively for each resulting half, too. This approach will be faster than the previous methods, but it’s not guaranteed to catch all of the collisions.

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另外的隐藏的问题是 collide_with_other_objects ()例程，它检查一个对象是否在场景内与任何另外的对象交叉。如果我们的场景有很多物体时，这例程会变得更重要。如果我们需要在场景对所有的别的对象检查，我们将粗略地做
Another hidden problem is the collide_with_other_objects() routine, which checks whether an object intersects any other object in the scene. If we have a lot of objects in the scene, this routine can get very costly. If we have to check each object against all other objects in the scene, we’ll have to make roughly

图三

(N choose 2 )的比较。因此，我们将要完成的工作就是比较数字的关系N2 (or O(N2))。但是我们能避免施行 O ( N2 )在若干方法之一的对明智的比较。例如,我们能把我们的世界划分成是静止的物体( collidees )并且移动的物体( colliders )的初速度 v=0 。例如，在一个房间里的一面僵硬的墙是一碰撞面和向墙被扔的一个网球球是一碰撞对象。我们能建立一个二叉树(为每个组的一个)给这些对象，并且然后检查哪个对象确实有碰撞的机会。我们能甚至进一步限制我们的环境以便一些碰撞对象不会与我们没有在 2 颗子弹之间计算碰撞的对方发生抵触，例程。当我们继续前进，这个过程将变得更清楚，为现在，让我们就说它是可能的。（为了减少场景方面数量的另外的方法就是建立一个八叉树，这已经超出这篇文章的范围，但是你可以在文末参看我给你列出的参考文献）现在让看看基于portal-based引擎的碰撞检测。
(N choose 2) comparisons. Thus, the number of comparisons that we’ll need to perform is of order N2 (or O(N2)). But we can avoid performing O(N2) pair-wise comparisons in one of several ways. For instance, we can divide our world into objects that are stationary (collidees) and objects that move (colliders) even with a v=0. For example, a rigid wall in a room is a collidee and a tennis ball thrown at the wall is a collider. We can build two spatial trees (one for each group) out of these objects, and then check which objects really have a chance of colliding. We can even restrict our environment further so that some colliders won’t collide with each other — we don’t have to compute collisions between two bullets, for example. This procedure will become more clear as we move on, for now, let’s just say that it’s possible. (Another method for reducing the number of pair-wise comparisons in a scene is to build an octree. This is beyond the scope of this article, but you can read more about octrees in Spatial Data Structures: Quadtree, Octrees and Other Hierarchical Methods, mentioned in the “For Further Info” section at the end of this article.) Now lets take a look at portal-based engines and see why they can be a pain in the neck when it comes to collision detection.

Skt32 2003-10-11

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高级碰撞检测技术　第一部分

高级碰撞检测技术　第一部分
Advanced Collision Detection Techniques

这文章原载于Gamasutra，共有三部分。我想将它翻译，请大家指教。

http://www.gamasutra.com/features/20000330/bobic_01.htm
http://www.gamasutra.com/features/20000330/bobic_02.htm
http://www.gamasutra.com/features/20000330/bobic_03.htm

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自从电脑游戏降临以来，程序员们不断地设计各种方法去模拟现实的世界。例如Pong（著名的碰球游戏），展示了一个动人的场面（一个球及两根摆绳）。当玩家将拽住摆绳移动到一定高度的，然后放开球，球就会离开玩家向对手冲去。以今天的标准，这样的基础操作也许就是原始碰撞检测的起源。现在的电脑游戏比以前的Pong复杂多了，而且更多是基于3D的。这也使3D碰撞检测的困难要远远高于一个简单的2D Pong。一些较早的飞行模拟游戏说明了糟糕的碰撞检测技术是怎样破坏一个游戏。如：当你的飞机撞到一座山峰的时候，你居然还可以安全的幸存下来，这在现实中是不可能发生的。甚至最近刚出的一些游戏也存在此类问题。许多玩家对他们喜爱的英雄或是女英雄部分身体居然可以穿过墙而感到失望。甚至更坏的是玩家被一颗没有和他发生碰撞关系的火箭击中。因为今天的玩家要求增加唯实论的要求越来越高，我们游戏开发者们将尽可能在我们的游戏世界做一些改进以便接近真实的世界。
　　Since the advent of computer games, programmers have continually devised ways to simulate the world more precisely. Pong, for instance, featured a moving square (a ball) and two paddles. Players had to move the paddles to an appropriate position at an appropriate time, thus rebounding the ball toward the opponent and away from the player. The root of this basic operation is primitive(by today’s standards) collision detection. Today’s games are much more advanced than Pong, and most are based in 3D. Collision detection in 3D is many magnitudes more difficult to implement than a simple 2D Pong game. The experience of playing some of the early flight simulators illustrated how bad collision detection can ruin a game. Flying through a mountain peak and surviving isn’t very realistic. Even some recent games have exhibited collision problems. Many game players have been disappointed by the sight of their favorite heroes or heroines with parts of their bodies inside rigid walls. Even worse, many players have had the experience of being hit by a rocket or bullet that was “not even close” to them. Because today’s players demand increasing levels of realism, we developers will have to do some hard thinking in order to approximate the real world in our game worlds as closely as possible.

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这篇碰撞检测的论文会使用一些基础的几何学及数学知识。在文章的结束，我也会提供一些参考文献给你。我假定你已经读过Jeff Lander写的图形教程中的碰撞检测部分(“Crashing into the New Year,” ; “When Two Hearts Collide,”; and “Collision Response: Bouncy, Trouncy, Fun,” )。我将给你一些图片让你能快速的联系起核心例程。我们将要讨论的碰撞检测是基于portal-based 及BSP-based 两种类型的引擎。因为每个引擎都有自己组织结构，这使得虚拟世界物体的碰撞检测技术也不尽相同。面向对象的碰撞检测是使用得比较多的，但这取决于你的现实可实性，就想将引擎分成两部分一样。稍后，我们会概述多边形碰撞检测，也会研究如何扩展我们的弯曲物体。
This article will assume a basic understanding of the geometry and math involved in collision detection. At the end of the article, I’ll provide some references in case you feel a bit rusty in this area. I’ll also assume that you’ve read Jeff Lander’s Graphic Content columns on collision detection (“Crashing into the New Year,” ; “When Two Hearts Collide,”; and “Collision Response: Bouncy, Trouncy, Fun,” ). I’ll take a top-down approach to collision detection by first looking at the whole picture and then quickly inspecting the core routines. I’ll discuss collision detection for two types of graphics engines: portal-based and BSP-based engines. Because the geometry in each engine is organized very differently from the other, the techniques for world-object collision detection are very different. The object-object collision detection, for the most part, will be the same for both types of engines, depending upon your current implementation. After we cover polygonal collision detection, we’ll examine how to extend what we’ve learned to curved objects.

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重要的图片
编写一个最好的碰撞检测例程。我们开始设计并且编写它的基本程序框架，与此同时我们也正在开发着一款游戏的图形管线。要想在工程结束的时候才加入碰撞检测是比较不好的。因为，快速的编写一个碰撞检测会使得游戏开发周期延迟甚至会导致游戏难产。在一个完美的游戏引擎中，碰撞检测应该是精确、有效、而且速度要快。这些意味着碰撞检测必须通过场景几何学的管理途径。蛮力方法是不会工作的 — 因为今天，3D游戏每幀运行时处理的数据量是令人难以置信的。你能想象一个多边形物体的检测时间。
在一个完美的比赛发动机,碰撞察觉应该是精确,有效,并且很快的。这些要求意味着那碰撞察觉必须仔细到景色被系住几何学管理管道。禽兽力量方法嬴得’t 工作—今天’s 3D 比赛每框架处理的数据的数量能是介意犹豫。去是你能核对对在景色的每另外的多角形的一个物体的每多角形的时间。
The Big Picture
To create an optimal collision detection routine, we have to start planning and creating its basic framework at the same time that we’re developing a game’s graphics pipeline. Adding collision detection near the end of a project is very difficult. Building a quick collision detection hack near the end of a development cycle will probably ruin the whole game because it’ll be impossible to make it efficient. In a perfect game engine, collision detection should be precise, efficient, and very fast. These requirements mean that collision detection has to be tied closely to the scene geometry management pipeline. Brute force methods won’t work — the amount of data that today’s 3D games handle per frame can be mind-boggling. Gone are the times when you could check each polygon of an object against every other polygon in the scene.

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让我们来看看一个游戏的基本循环引擎。（Listing 1）
http://www.gamasutra.com/features/20000330/bobic_l1.htm
这段代码简要的阐明了我们碰撞检测的想法。我们假设碰撞没发生并且更新物体的位置，如果我们发现碰撞发生了，我们移动物体回来并且不允许它通过边界（或删除它或采取一些另外预防措施）。然而，因为我们不知道物体的先前的位置是否仍然是可得到的，这个假设是太过分简单化的。你必须为这种情况设计一个解决方案（否则，你将可能经历碰撞而你将被粘住)。如果你是一个细心的玩家，你可能在游戏中会注意到，当你走近一面墙并且试图通过它时，你会看见墙开始动摇。你正在经历的，是感动运动返回来的效果。动摇是一个粗糙的时间坡度的结果(时间片)。
Let’s begin by taking a look at a basic game engine loop (Listing 1). A quick scan of this code reveals our strategy for collision detection. We assume that collision has not occurred and update the object’s position. If we find that a collision has occurred, we move the object back and do not allow it to pass the boundary (or destroy it or take some other preventative measure). However, this assumption is too simplistic because we don’t know if the object’s previous position is still available. You’ll have to devise a scheme for what to do in this case (otherwise, you’ll probably experience a crash or you’ll be stuck). If you’re an avid game player, you’ve probably noticed that in some games, the view starts to shake when you approach a wall and try to go through it. What you’re experiencing is the effect of moving the player back. Shaking is the result of a coarse time gradient (time slice).

skywind 2003-10-09

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当检测到有碰专的时候，先把接触他的球求解出来，根据物理的矢量动量公式
以及能量首恒公式可以求解后来的动量，但是由于球的质量都是固定的，所以可以
方便的认为速度都是平分的，能量也是平均分配的，所以可以很大程度上面化解
这个算法，不过再怎么说，扎实的线性代数基础是必备的 -_-

AngelGavin 2003-10-09

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BlueSky2008 2003-10-09

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平面球体碰撞的算法:两体问题好解，三体或三体以上就不好算了。

NowCan 2003-10-09

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根据物理定律做。当成刚体碰撞来作。我得想想。

[高分求算法]平面球体碰撞的算法，比如台球游戏中球之间的碰撞。

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