View-Dependent Geometry

Problem and definition

Paul Rademacher original article synthesis. Ludovic Gu´ egan

Context of application

TV cartoons speak to young children trough their imagination. In this way, the all environment is exaggerated: colors, shapes, actions... One can notice that most of these world ”deformations” can be more or less reproduced by computers when they render keywords: Cartoon animation, 3D animation, cartoon animations. In this paper we will try to anrendering, animation system, non-photorealist ren- swer one of the most critical aspect, the model gedering, 3D blending ometry (mesh) accentuation. Because the modeling process often start by a 2d study, our method will be based on. One can notice that artists use to work around some reference views. And these views might Abstract introduce aesthetic distortions (like perspective exThis article introduce a new method to produce and aggeration). render models enhance by view-dependent geometries. This is especially usefully in cell animation in order to show artistic distortions. From some refer- Geometric view-specific interaction ence drawings one construct several models associ- In order to render comparable effets we will capture ated with key-viewpoints. Then any particular view severals models associated with their points of view. of the model will be associated with a specific mesh In this way we will be able to ”merge” the models according to the following algorithm: (1) Find the according to these point of views. As a result we will appropriate key-viewpoints for the camera. (2) Com- be able to interpolate the model geometry at ruining pute the weights of the key-viewpoints. (3) Blend time. key-viewpoint’s models according to their weights. This design is available for both rigid and animated models.

Rigid models

Creating the views

R´ esumer

A 3d model and its different associated captures looks are need to start producing new models. To achieve this, lets consider some limitations: (1) We supposed that the distortions doesn’t changed the model topology. (2) These moves are small enough not to generate incoherent model (think about a boot lace). (3) Reference drawing’s view allways point the object center. So we will construct one new model per 2d reference drawing. For each one we process as followed: (1) We put on top of the drawing the basic 3d model and turn it to fit the view. (2) We handle distortions (or diferencies) by moving the 3d model vertices to make them correspond to the draw. Note that there is no correspondence in the 3d space but

Nous allons introduire une m´ethode permettant d’afficher un mod`ele g´eom´etrique en fonciton de l’angle de vue. Ceci peut ˆetre utilis´e dans la synth`ese d’animation lorsque des effets artistiques sont attendues. A partir de profils types il est possible de construire des mod`eles associ´ees aux vues pr´ed´efinies. L’algorithme pour effectuer le rendu du le maillage est d´ependant du point de vu, le voici: (1) D´eterminer les points de vues clefs proches de la cam´era. (2) Calculer les coeficients qui leurs sont associ´es. (3) Ponderer les mod`eles en fonction de ces co´eficients. Ce mod`ele fonctionne de la mˆeme mani`ere pour les animations. 1

Animated meshes

just in the view projective plane. If Z-depth coherence problem appear it is possible to handle it, but this is not the purpose. Once again, we just try to make the model fit the draw for the specific view, we do not manage volumes. As a result we obtain severals models associated with severals key-viewpoints.

Pre-calculated models

Lets call a key deformation a model geometry associated to a key-viewpoint. The principle of animated view-dependent model is to obtain for each frame all the key deformations. In this case we can apply the previous algorithm. Of course we are not going to creInterpolations ate the key deformations frame by frame. Once again we will interpolate the key deformations produced To render correctly the model according to a given for some particular frames. For an cycled animation camera position, we will interpolate the previous pro- of 40 frames, two key viewpoints and two snapshots duced models. Basically we just blend coresponding (frame 10 and 30) could be enough. So what we need vertices as we have kept the model convexity. The is: (1) an animation (2) 4 reference drawings. To issue is to compute the pondering factors depending preserve the underlying motion we won’t just interon which key viewpoints are the more relevant. As a polate vertices. Instead, for each key-viewpoints we result one key-viewpoints is associated with a scalar will compute for each vertex the deformation offset value named its weight. It is assume, without ex- to the basic object. Then a natural cubic spline will planation, that the model geometry only depends on reconstruct missing frames key-deformations. the view direction and not its distance. Lets remarks that another algorithm could consider both distance Runtime computations and direction in the choice of the interpolation mechanism. To select the key-viewpoints involved in the This part is now exactly the same as in the previrepresentation of a specific view position we compute ous section. From the time each frame has its keythe convex hull formed by all the key-viewpoints. If it deformations it may be render like a rigid model. doesn’t surround the base object, new artificial key- In the previous example, this would gave us one 40 viewpoints are needed. The convex hull give us the frame basic object, and two others 40 frames models triangle made of key-viewpoints (v1 , v2 , v3 ) with the ready to be render. closest direction to the camera. Thus we can easly compute which triangle (of the convex hull) intersect the camera-object line. So we can have the 3 Conclusion and Prospects barycentric weights (wi ) corresponding to the 3 keyThis method is well adapted for people who alviewpoints (vi ). In order to have smoother triangle ready have reference drawings of their models. But transition we scale this weights according to (1). the very sensible part is the manual creation of the view-dependent models (creating the views), and any 0 wiα + (semi)automatic system would be of great help. This (with α ∈ R ) (1) wi = w1α + w2α + w3α method is made to produce at runtime a specific 0 0 0 v = w1 v1 + w2 v2 + w3 v3 (2) model so it is widely useless in the case of fixed or known paths. Also this method has a hight memory cost, but creNow the view specific representation is given by movates a specific view-dependent model in θ(n), where ing each point v of the basic model following the equan is the number of vertices in the model. Thus this tion (2). This way a new geometric model is produce may allow real-time application, but in this case it for each camera position. This technical is usefully might introduce complicated issues due to the mesh for models like buildings or scenery, but need to be integrity. improved to handle animations. 2