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The Renderer dock is organized around three independent choices: the rendering style of the surface, the edit target that the colors and textures act upon, and — on multi-mesh surfaces — the scope those controls apply to.

This selects how the surface itself is drawn. The three modes are mutually exclusive:

• Base: Flat color (fast).
• Phong: Realistic specular lighting.
• WireFrame: Displays the polygonal grid. The overall fineness of that grid is set by Steps in the Equations dock (more steps → denser wireframe). When this mode is active, the Density u and Density v controls also become enabled: they do not add resolution, they only rebalance the two families of coordinate lines relative to each other. This is useful when the surface shape stretches one parameter far more than the other (long tubes, thin ribbons), leaving the U-lines and V-lines looking visually mismatched — you can thin out the crowded family or thicken the sparse one to even out the appearance, without changing the geometry. They are greyed out in any other mode (and in Ray Marching, where wireframe is not available).

Implicit surfaces are lit by two fixed lights, one from the side and one from behind. Between them they leave some faces dark whatever you do: the inside of a cavity, a tube seen down its own axis, a face turned edge-on to the view. The Headlight slider adds a third light that comes from the observer, so it always illuminates what you are looking at — which is exactly what a cavity needs.

It is off at zero, which is the default, and there the image is identical to the one before this slider existed. Raise it only when something you want to see is in shadow; it deliberately ignores ambient occlusion, because the places that need filling are the ones where occlusion is strongest. The value is saved with the scene.

A surface built from several independent grids (see Multi-Mesh Surfaces in the Script Guide) can be styled grid by grid. The Multi Mesh box decides the scope of the appearance controls — colour, transparency, Light Intensity and the Solid/Phong/WireFrame choice:

• All: the surface behaves as a single one. Every control applies to all the grids at once, whatever they were set to individually.
• Mesh: the spin box next to it picks one grid, and the same controls act only on that one — including its own Density u / Density v, so two grids can be drawn as wireframe with different line spacing.

Switching to All does not erase what you set per grid: those values are only suspended, and they come back exactly as they were when you switch to Mesh. A grid you never touched simply follows the global settings, so surfaces made of a single mesh — and every preset built before this feature — behave as they always did. Both the per-mesh appearance and the active scope are stored in the preset.

Below the selector, four fields set the parametric domain — the portion of the surface each grid actually draws. They follow the same scope rule as the controls above, and they take the same expressions as the U/V limits of the Equations dock (numbers, pi, tau, the constants A–F and S):

• Mesh: the domain belongs to the selected grid alone. Halving v_b draws half of that grid and leaves the others whole — a way to open a figure up and look inside it without touching the script.
• All: the four fields drive a domain of their own that applies to every grid at once. It suspends the individual domains instead of overwriting them: restrict two grids, switch to All and the figure comes back whole (or cut as you last left it in All), cut it there, then switch back to Mesh and the two restrictions are still exactly where you put them.

Unlike the appearance controls, a domain generates the vertices, so each change rebuilds the grid. The fields confirm on Enter or when they lose focus, and they apply at once — there is no Run to press.

The value you type wins over the script. A grid whose domain you edited keeps it through Master START, both Run buttons, an Enter in the equation fields and a reload, and it is saved in the preset. The trade-off is that such a grid stops following its own //MESH_BEGIN section: editing that section in the script no longer changes it. To hand the grid back to the script, type the values its //MESH_BEGIN block declares — or load the preset afresh, which restores the declared domain for every grid you never customized.

Note: the U/V limits in the Equations dock govern single-mesh surfaces. On a multi-mesh surface each grid carries its own domain, so those fields no longer drive the geometry — these do.

Note: a per-mesh colour has no effect while a texture is active on the surface, because the texture carries its own colours (see the u_col1 token in the Script Guide).

This pair of buttons is a single exclusive choice that decides what the color sliders, the Texture checkbox and the Library textures act upon. Switching the target never changes the rendering style above — the two are completely separate axes.

• Surface: Colors and textures are applied to the 3D/4D surface itself. This is the default.
• Background: Everything is redirected to the 2D interactive environment drawn behind the objects. While this target is active, images and procedural effects stay fully interactive — you can pan, zoom and rotate them with the mouse, just like the 3D camera. The surface is not hidden: only the editing focus moves to the background, so you can keep Surface one click away.

Note: If no background image is explicitly loaded, a fallback procedural Deep Space gradient will be automatically generated to ensure a sleek presentation.

Textures (both procedural scripts and static images) follow whichever edit target is selected:

• Surface Textures: With the Surface target selected, applying a texture from the Library (or activating the Texture checkbox) wraps the selected image or script directly onto the geometry of the 3D/4D surface. This works in both the Base and Phong rendering styles; in WireFrame the surface texture is hidden and the sliders edit the line color instead.
• Background Textures: With the Background target selected, any texture you load or procedural script you run is applied to the 2D background behind the surface, where it remains fully interactive (pan, zoom, rotate).

When a colored procedural texture is active, the Color 1 and Color 2 buttons appear and let the sliders edit the two tint slots of that texture. In the Surface target, picking Color 1, Color 2 or Surface is a single mutually-exclusive choice of what the sliders control; in the Background target, Color 1/Color 2 instead drive the two background-texture colors.

Besides loading images (PNG/JPG), you can write custom GLSL scripts to generate mathematical textures in real-time.

// Example Texture Script
float r = sin(u * 10.0);
float g = cos(v * 10.0);
return vec3(r, g, 0.5);

Procedural textures can be given to one grid at a time, but images behave differently: an image is a single graphics resource shared by the whole surface, not code that can be duplicated per grid. Loading one from the Library therefore always covers the entire surface, even when the Multi Mesh scope is set to Mesh. The application says so with a one-off notice the first time it happens.

The way to bring an image onto a single grid is the Animated Images folder, under Textures > Procedurals in the Library. These are procedural scripts — so they do apply per mesh — that redisplay the image already loaded rather than generating a pattern of their own. Two steps:

1. With the scope on All, load the image from Textures > Images as usual.
2. Switch to Mesh, select a grid, and apply one of the Animated Images presets.

Repeat the second step on each grid that should display the image. Every grid keeps its own framing and its own movement, and the ones you leave alone stay in plain colour — so the same photograph can drift on one branch of a surface and rotate on another. A grid that already carries a texture of its own keeps showing that one.

Choosing the preset. Still Image shows the picture motionless and is the one to use for a simple per-mesh image. Drifting, Rotating, Breathing, Shearing and Squished animate it in different ways — sliding, turning, pulsing, slanting and stretching respectively. Each script carries a short block of parameters (speed, amount) at the top of its code, so the effect can be tuned in the Script dock without rewriting anything.

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