Piecewise Continuous Anchoring

If N instances are given, it is theoretically possible to use N-1 anchor origins to define a deformation that would result in the N given forms at the corresponding aspect ratio factors. Just as in curve fitting, we would not fit a (n-1)th degree polynomial to a set of n points because of the over-crookedness of the resultant curve and the lack of localized control over the curve. Instead of determining the multi-level anchor origins which are the coefficients of the two continuous parametric...

Review on Skeletal Stroke Deformation

The skeletal stroke deformation has been discussed in detail in 28 , here we will only briefly go through the main points but leave out the mathematical details and derivations. The skeletal stroke deformation is based on localized parametric coordinate system transformation along the stroke application path. A skeletal stroke is defined by specifying a reference backbone and a reference thickness on any arbitrary picture. The purpose of defining the reference backbone and thickness is for...

Speed Lines for Motion Blurring

In both comics and animation, fast action is often represented by speed lines, which suggest the distance an object or character has travelled across the camera before its shutter is closed again. Motion blurring is particularly important in animation because it reduces temporal aliasing effects. Its method of generation in vector based cartoon has not been, however, a well addressed problem. One possible way is to employ temporal antialiasing techniques like stochastic sampling across the time...

Rendering a Recursive Stroke

Rendering a recursive stroke explicitly by determining the resultant geometry is in general impossible. Since a recursive stroke is equivalent to an IFS (Iterated Function System) code (with a condensation set if objects other than itself are present in the definition) 3,4,5,6 , the attractor is often a fractal with a fractal dimension less than 2. We therefore have to resort to one of the approximation methods for rendering these fractals. The Escape Time Algorithm 4 would result in a clean...

Controlling a PseudoD Stroke

We have demonstrated how to create an illusion of rotation by making use of the general anchoring mechanism. To perform that deformation, only one control parameter, the aspect ratio of the stroke, has been used. We could in theory control any kind of deformation of a picture with the aspect ratio alone. If different features in a picture are to change in different ways, however, it would be more convenient to have independent controls. easily set up an external control system by which users...

General Drawing Applications

We anticipate that skeletal strokes would have considerable impact on many drawing applications in fashion design where stylish bold strokes are often used in interior design where pseudo-3D strokes representing furniture and architectural objects can be laid out with ease in dynamic clip-arts which can deform dramatically beyond the limits of stretching, shrinking, shearing, twisting and bending. If implemented in windowing system kernels or page description languages like PostScript, the...

Animation with Skeletal Draw

Animation takes full advantage of the picture and deformation abstraction capability provided by skeletal strokes. The Skeletal Draw program has also been built with facilities to generate animation sequences. Traditional key-frame technique is used by Skeletal Draw. To create the key-frames, the user directly manipulates the characters in the scene. The system then calculates the in-betweens by interpolating Catmull-Rom splines. After the keyframes have been laid out, the program can do a...

Skeleton verses Envelope

Many drawing 2D warping packages allow the user to specify the deformation of a picture by reshaping an envelope around the undeformed picture. This technique has been advocated for applications in 2D animation in as early as the 70's 15 and is still widely used in the latest systems 32 . A coordinate system transformation based on envelope deformation is quite different from a skeleton based one. The former is much more well defined as the coordinates within an envelope can usually be...