Our idea is motivated by a drafter's device called the French curve. The advantage of French curves is that they provide templates for tracing out curves, without drawing them freehand. Our project considers its analogue in one higher dimension, namely 3D surfaces. A predefined set of surfaces, called French surfaces, is given to the user to choose from. The selected surfaces are then blended together one after another to form the final model. The system F RENCH S URFACES suggests a breakthrough way of surface design in computer graphics. We depart from the traditional approach where users actively draw surfaces, to one where users just choose surfaces from a big library. Also, our system avoids the not-so-user-friendly mathematical structures and freehand controlling of traditional methods. The only input from the users is their artistic expressions, but not their math skills. FRENCH SURFACE A New Technique for Surface Design Zita Cheng CHOOSE A SURFACE FROM THE SAMPLES ON THE CONTROL PANEL AS A STARTING POINT. O The predefined set of French surfaces must be large enough so that surfaces of any curvature can be formed, but small enough to allow easy searching. O We come up with a minimal set of French surfaces which consists of the following primitive shapes: ellipsoids, paraboloids, cones, sharp tips, various cylinders, wedges, torii, and spirals, all of adjustable size, thickness, extent, tilt, and degree of bending (Fig 2). O Theoretically, this set of primitive surfaces, together with the blending technique, is enough to form any surface. O A sampling of this set is used as a starting point for traversing the space of French surfaces. They are characterized by two axes: one from bumps to elongated surfaces, and the other from round to sharp shapes (Fig 1). O Our triangle mesh design satisfies the area curvature rule: the area of any triangle is inversely proportional to the local curvature. E.g., Fig 3b satisfies the rule while Fig 3a does not. SEARCH THE SPACE OF FRENCH SURFACES, USING SCALE- BARS AND BUTTONS, FOR THE ONE YOU WANT. O With the chosen surface as a starting point, the user can traverse the space of French surfaces by adjusting the scale-bars and buttons (Fig 4). O Each French surface has its own set of scale-bars and buttons. O Users are virtually stretching, or cropping a cone, extending the ring of a torus, controlling the angle of a wedge, or bending a cylinder (Fig 5). O The Range button allows users to toggle between coarse and fine scaling. The Lock check box gives the options of scaling each direction individually or scaling the surface as a whole. O The system accumulates changes. E.g., if you first tilt a cylinder, then you bend it, the result of blending is not a torus, but a spiral of the corresponding scales. O Human psychology and H.C.I. Principles are considered in the design of the technique of navigation. CHOOSE THE DEGREE OF BLENDING. PRESS BLEND TO SEE THE BLENDING RESULT. IF SATISFIED, PRESS CONFIRM. ELSE, READJUST THE POSITION, THE PARAMETERS, OR THE DEGREE OF BLENDING. O The blend-surface is formed by a family of bezier curves. O The degree of blending is adjustable. This is done internally by changing the number of control points of the Bezier curves (Fig 10). O Rays with adjustable length from the rim of the surface serve as a guide for positioning (Fig 11). O Blending is the spirit of our system. Our design of the blending algorithm is original. We utilize tools from differential geometry, numerical analysis, and data mining. O One feature of our system is that blending will not affect the shape of the French surface or the model. O Users can also “walk around” the model to examine the geographical relation between the surface and the model (Fig 8). O Users can adjust positioning at the same time they adjust the parameters of the surface. O We employ trackball motion using the mouse. Users can adjust the position of the chosen French surface relative to the ongoing model by rotations and translations (Fig 7). POSITION THE SELECTED FRENCH SURFACE RELATIVE TO THE MODEL STEPS surface model translation rotation Examples of artwork. (a) Multi-Blend, showing the power of blending; (b) Wireframe Piggy; (c) Piggy; (d) C for Castle. Fig 1: Stating-point-surfaces on the control panel. Fig 2: Examples of French surfaces. Fig 3: Only (b) satisfies the area curvature rule. Fig 4: Scale-bars and buttons on the control panel. Fig 5: Examples of stretching, cropping, extending, tilting, and bending. Fig 7: Trackball motion to position the surface. Fig 8: “Walk around” to examine the relative position of the surface to the model. Fig 12: The blending result. Fig 11: Rays from the rim serve as a guide. Fig 9: Control panel for blending. Fig 10: Bezier curves with 2 control points at P (red) and 3 control points at P (green). P rounder blending tighter blending Human Communications Technology Lab, University of British Columbia, Vancouver, Canada. a b