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Digital Dream Studio V2
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About existing plug-ins

 

About existing plug-ins

Mapping

Mapping is the distortion of an image. Technically, every pixel in the distorted image is linked to a corresponding pixel in the original image. The correspondence is translated in mathematical equations. Some problems arise, such as the need for interpolation in between pixels and the need for extrapolation for data that exits the domain.

The methods for defining mapping available in this plug-in is Analitical definition, Ordinal Differential Equation definition and Height Map definition.

Also the plug-in allows the overlaying of several mappings, thus generating all kinds of simple or complex motion blurs. One can imagine motion blur as keepin the shutter of a camera open, while photographing the pixels of a canvas, each one moving on a defined trajectory.

Dynamic Mapping

The Dynamic Mapping plug-in has the same concept as Mapping: distorting an image by using a map. However, in DMapping the user may interactively edit the map by using different tools.

The same problems regarding interpolation and extrapolation arise, and they are solved basically in the same way.

The map used for distorsion can be loaded from or saved to a file, compatible with the Mapping plug-in.

DMapping also support bitmaps in 32bit format, including Alpha channel.

The tools available for editing the map are:

  • Click Mapping - Mapping applyin on mouse click
  • Mouse Mapping (Airbrush style) - Mapping independent of mouse events
  • Freeze - allows selecting a frozen area that is not to be affected by other mapping tools
  • Undo - allows the partial or complete restoration of the image.
  • Exact applying - allows the applying of a click mapping effect on an exact contour (rectangle, ellipse, line etc).
  • PDE Simulation - interesting editing of maps using user-defined Partial Differential Equations

Fractal

The word fractal originates from the latin "fractus", which means severed or broken. Fractals are actually a form of chaos. They have many different forms (IFS, L-Systems, ODE, PDE), but as they were initially defined by Benoit Mandelbrot, they represent visualizations for stability analyses of ordinal differential equations (ODE).

What one does if take a system of ODE, set a fairly large differential step (usually 1) and the initial conditions. The iterations commence and a response is given in regard to how long it lasts until the values of the solution exit a certain region of space. If a certain number of maximum iterations is reached, the iterations are stopped. So, if the region is exited in the first iteration, the pixel shall be black and if it remains within the region until the maximum number of iterations, it is white. For in-between values, it will have a shade of grey.

The widely-known methods for rendering these fractals are Julia and Mandelbrot. Both of them colour each point in space according to how the chaotic system "behaves" at that point. The Julia method takes the coordinates of the point and plugs them as initial conditions for the system, as system parameters remain constant. Mandelbrot is the other way around.

Aside from being beautiful, fractals have some visual proprieties: they are self-similar and infinitely irregular. No matter how much it is zoomed in, a fractal still presents smaller and smaller asperities.

This program allows the user to set up the chaotic system in detail and to plot it according to some specific settings.

Partial Differential Equations

Partial Differential Equations are a very useful mathematical tool and physics and other scientific fields. In this case, PDE are used only as a source of chaos. Initial conditions are loaded from a bitmap file. One must specify the differential step considered (IT IS HIGHLY RECOMMENDED THAT IT IS KEPT BELOW 0.5) and the number of steps to be taken. Three channels mean three different sets of initial conditions, that need to be solved separately - so each one can be solved with different parameters. By clicking the "Simulation" button, the resolution of the equation commences and the solution is progressively displayed as it evolves (using the specified refresh rate).

Data can be saved as bitmap, whether the program is used as a plug-in or as stand-alone.

The Wave Equation is a second order PDE describing the motion of an elastic membrane, initially deformed as specified by conditions. The waves propagate at a certain speed (v) and with dynamic damping (loss of energy - k). These two parameters can be specified for each channel. Also, esential to the form of the solution are the rectangular boundary conditions, normally set to "Clammed". However, for diversity, one may attempt setting them on "Wrap" or "Mirror". It is mathematically possible, though improbable for the values to be slightly out of range - in this case they will be truncated. The "Normalize" button brings all values in range, without truncation.

The Diffusion Equation describes diffusion in a moving fluid. If fluid speed is set to zero, the process will result in a progressive blurring, asymptotically converging to the mean value (or in this case, the mean color). The parameter v, in this case, is the coefficient of diffusivity and vx and vy respectively specify the equations of the fluid motion, in regard to time and space. One should be warned: in this case, if a too large differential step is specified or if certain parameters become too large, the PDE system may become unstable and diverge.