Extracting Camera-Control Requirements and CameraMovement Generation in a 3D Virtual Environment

Hirofumi Hamazaki1, Shinya Kitaoka1, Maya Ozaki1,Yoshifumi Kitamura1, Robert W. Lindeman2, Fumio Kishino1

1 Graduate School of Information Science and Technology, Osaka University2-1 Yamada-oka, Suita, Osaka, 565-0871, JAPAN

{hamazaki.hirofumi | kitaoka.shinya | ozaki.maya | kitamura | kishino}@ist.osaka-u.ac.jp

2 Department of Computer Science, Worcester Polytechnic Institute100 Institute Road, Worcester, MA 01609, USA

gogo@wpi.edu

ABSTRACTThis paper proposes a new method to generate smooth cam-era movement that is collision-free in a three-dimensionalvirtual environment. It generates a set of cells based oncell decomposition using a loose octree in order not to in-tersect with polygons of the environment. The method de-�nes a camera movement space (also known as Con�gurationSpace) which is a set of cells in the virtual environment.In order to generate collision-free camera movement, themethod holds a path as a graph structure which is basedon the adjacency relationship of the cells, and makes thecamera move on the graph. Furthermore, by using a poten-tial function for �nding out the force that aims the camera atthe subject and a penalty function for �nding out the forcethat restrains the camera on the graph when the cameramoves on the graph, we generate smooth camera movementthat captures the subject while avoiding obstacles. Severalresults in static and dynamic environments are presentedand discussed.

Categories and Subject DescriptorsH.5.4 [Information Interfaces And Presentation]:Hypertext/Hypermedia

General TermsAlgorithms, Design, Human Factors

Keywordsvideo game, virtual reality, camera control, path planning,octree, interactive system

1. INTRODUCTIONIn recent years, applications like games and Second Lifewhich allow a user to explore a three-dimensional (3D) vir-tual environment have emerged. These applications createcamera movement such as translation, rotation, and zoomaccording to the character's movement. Also as in tradi-tional camera movement, the camera is manipulated to keepfollowing the character in a 3D virtual environment. Thisgives the character manipulator a deeper realistic sensation.But if the camera just keeps following the character, it some-times may penetrate a building or go under the ground inthe virtual environment, or it may not capture the characterdue to obstacles which exist between it and the character.In order to avoid these cases, we have to set control require-ments relating to camera movement, depending on the goalof the virtual environment.

On the other hand, the study of avoiding collisions with ob-stacles has been carried out in robotics, for example, PRM(Probabilistic Roadmap Method) [1, 2] and RRT (Rapidlyexploring Random Trees) [3, 4]. Also, The cell decomposi-tion methods which create a roadmap graph to avoid colli-sions with obstacles are famous ones. The cell decompositionmethods divide an environment into equal-sized cells [5, 6]or varying-sized cells based on an octree [7, 8], and pick aset of cells which is collision-free with the obstacles. Then,these cells are connected with nearby cells, and the roadmapgraph is created. By moving on the roadmap graph, robot'smovements become collision-free.

Therefore, we propose methods for e�ciently automatingthe process of determining legal camera movement based oncamera-control requirements by extending the cell decompo-sition methods. By automatically creating a roadmap graphthat is a collision-free space between the camera and the ob-stacles from the virtual environment based on hierarchicalcell decomposition using a loose octree [9] not just an octree,then making the camera follow the subject smoothly in thisspace, we can automatically generate the camera movementthat ful�lls the control requirements.

Figure 1: Procedure of creating a camera movement space in the case of a maximum octree depth of two. (a) Make a cell thatcontains the obstacle; (b) Create four more new cells by evenly dividing the cell (actually create eight new cells). New cell'scolors are di�erent (the top left is red, the top right is blue, the bottom left is yellow, the bottom right is pink); (c) Enlargethe new cells respectively; (d) Detect the intersection between each cell and the obstacle, add the cell to the roadmap graphwhen the cell does not intersect with the obstacle, and restore the size of the cell when the cell intersect with the obstacle;(e) Create four new cells again by evenly dividing the cell that intersect with the obstacle; (f) Enlarge new cells again; (g)Remove the cells that intersect with the obstacle because depth of division reaches the maximum octree depth.

2. A CAMERA CONTROL METHODIn the camera movement generation process, it is importantto �gure out the camera movement space. However, becausethis space changes depending on the user's intention, wede�ne a camera movement space which is a collision-freespace between the camera and obstacles in the environment.This prevents the situation in which the camera penetratesobstacles and captures neither the subject nor the positionalrelationship between the subject and the environment. Wede�ne camera-control requirements as :

• The camera does not penetrate obstacles.

• The camera keeps following the subject.

To ful�ll this requirements, we extract a camera movementspace from the environment. Here, we describe a methodof extracting camera-control requirements and a method ofgenerating camera movement that meets the control require-ments.

Also, we support 3D virtual environments as follows :

• The number of cameras is one.

• The number of subjects is one.

• The subject's movement is unknown.

• The subject's orientation is not considered.

• The environment is constructed from polygon dataonly.

This enables us to focus on the movement of a chase camera.

2.1 Extracting Camera-Control RequirementsWe represent a camera movement space as a set of axis-aligned cells based on cell decomposition, and then createa camera roadmap graph using the adjacency relationshipof the cells. In this way, when a subject is contained in or

intersecting with a cell, we are assured of seeing the subjectif the camera reaches the cell because a cell is a convex hull.The method's procedure (Figure 1) is described as follows :

1. De�ne a maximum octree depth.

2. Make an axis-aligned cell that contains all obstacles.This cell is the octree's root.

3. Create eight new cells by evenly dividing the cell in thex-axis, y-axis, and z-axis (eight octants). Because thecell contains obstacles, we need to �nd out the cellsthat do not contain any obstacles.

4. Enlarge the new cells respectively. As a result, over-lapped regions of cells arise.

5. In each cell, detect the intersection between the celland the obstacles.

• Intersection case� If depth of division has not reached the max-imum octree depth, restore the size of thecell, create eight new cells by dividing the cellagain, and go to step 4.

� If depth of division reaches the maximum oc-tree depth, stop.

• Non-intersection case� The cell is added to the roadmap graph.

In this way, a camera movement space based on hierarchicalcell decomposition using a loose octree is created. A looseoctree does not only divide the region into eight cells but alsoenlarges each cell and creates overlapped regions of each cell.With overlapped regions, the cells are mutually adjacent andwe can create a camera movement space as a roadmap graph.

In addition, to speed up the intersection detection betweenthe cells and obstacles, we preliminarily manage the obsta-cles using an AABB (Axis Aligned Bounding Box) tree [10].

Figure 2: Shrine architecture (model by Marko Dabrovic)

2.2 Generating Camera MovementWhen the cell that overlays the camera is di�erent from thecell that overlays the subject, we de�ne these cells as thestarting point and the ending point. By making the cam-era move from the starting point to ending point on theroadmap graph, we generate camera movement that ful�llsthe camera-control requirements. For �nding the path onthe roadmap graph, we use the A∗ algorithm [11] becausewe can arbitrarily con�gure a cost function used for path�nding, and also can de�nitely �nd a path which has mini-mum cost. In this paper, we con�gure the cost function asthe Euclidean distance between the subject and the cells inthe camera movement space. Also, the A∗ algorithm is onlyused when the cell that overlays the subject changes due tomovement of the subject for reducing the cost of the path�nding.

The camera moves along the path that was found by theA∗ algorithm. However, the path is not composed of linesegments but a cell range, so we have to create a trajectoryfor the camera. In this paper, we obtain a trajectory whichis pursuant to Hooke's law by using a potential function for�nding out the force that aims the camera at the subject anda penalty function for �nding out the force that restrainsthe camera on the graph. This way, we generate cameramovement that is smooth and collision-free.

2.3 Resulting Camera MovementWe applied the proposed method to an environment with ashrine architecture (Figure 2). In this environment, we cre-ated a camera movement space, and then generated cameramovement that captures a moving subject in the environ-ment.

In Figure 3, we show the camera movement space that wascreated in the environment. The set of cells representedby the green line segments is the camera movement space.Figure 4 shows a camera trajectory created in the architec-ture. The purple cell is the ending cell of path �nding. Thegreen cell range represents a path in the camera movementspace, which was found by the A∗ algorithm. The red linethat extends to the side of the subject is the camera trajec-tory. In this example, using the Euclidean distance betweenthe subject and the cells of the camera movement space asa cost function, we sought a path which has the shortestmovement distance of the camera. Also, the camera trajec-tory shows that we did �nd the trajectory within the cellsof the camera movement space.

Figure 3: A created camera movement space in the environ-ment

Figure 4: Camera trajectory when the subject goes behinda pillar

3. DYNAMIC ENVIRONMENTSThus far, we have considered a static virtual environmentwithout movable obstacles. Next we describe how to adaptour proposed method to a virtual environment with mov-able obstacles (a dynamic virtual environment). We addthe constraints below for a dynamic environment.

• The number of obstacles ranges from dozens to hun-dreds.

• Obstacle movement is unknown.

• Obstacle shape is a rectangular solid.

In Figure 5, we show a dynamic virtual environment. Theorange objects are moving obstacles. To adapt our method,

Figure 5: Dynamic virtual environment

Figure 6: Camera trajectory in the dynamic environment

we slightly modify the method for extracting camera-controlrequirements and the method for generating camera move-ment.

First, to change the method for extracting camera-controlrequirements, we add the following processes.

• By detecting the intersections between the camera move-ment space created in a static environment and mov-able obstacles, cells intersected with the obstacles areexcluded from the camera movement space.

• If excluded cells no longer intersect with movable ob-stacles, the cells are restored to their previous cameramovement space.

Also, we perform the intersection detections in real time.By changing the camera movement space as a result of theintersection detections, a new camera movement space iscreated. However, if there exist many movable obstaclesin the environment, the cost for intersection detection forall obstacles is high. Therefore, we surround the camerawith a bounding box. Intersection detection between theobstacle and the camera movement space is performed whenthe obstacle intersects with this bounding box.

Next, we modify the method for generating camera move-ment. Because the camera movement space is changed inreal time to adapt to a dynamic environment, we have tore�ect this change in camera movement generation process.In a static environment, we use the A∗ algorithm only whenthe cell which overlays the subject changes. However, in adynamic environment, we use the A∗ algorithm at regularintervals. Also, because the camera movement space is rep-resented as a set of cells, there are margins for moving thecamera in the path. We therefore center a sphere with acertain size around a movable obstacle, and generate a re-pulsive force along the normal of the sphere's surface. Inthis way, every time the obstacle gets close to the camera, acamera movement is re�ected and avoiding obstacles is moresmoothly performed. We show a camera trajectory createdin the dynamic environment in Figure 6.

4. CONCLUSIONS AND FUTURE WORKIn this paper we have described the method to generatecamera movement based on camera-control requirements.First, we de�ned a camera movement space as a collision-freespace between a camera and obstacles in an environment,and camera-control requirements as the camera movement

space. Next we extracted the camera movement space as aroadmap graph that is created by hierarchical cell decompo-sition using a loose octree. We then found the path betweenthe camera and the subject within the camera movementspace. By controlling the camera on the path by a poten-tial function and a penalty function, we generated cameramovement that captures the subject while avoiding obsta-cles. We also adapted the methods to an environment withmovable obstacles.

In this paper, we have considered chase camera movement.In the future we will try to make a camera movement spaceby using a K-D tree and compare a K-D tree with an Octreeto examine which one is more suitable for environments. Inaddition, we plan to generate cinemagraphic camera move-ments which include panning that rotates the camera andcutaways that change the camera position. Our future workalso includes other camera-control requirement investiga-tion.

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