Z80 BBC BASIC - Emulated on Windows

Thursday, 22nd May 2008

I've started working with the actual BBC BASIC interpreter. As it won't run in its current state on the TI calculator (it relies on a jump table at &FF80..&FFFF to interact with the host, which is protected) I'm using the Z80 emulator I wrote for Cogwheel to try and puzzle out what the host interface should be doing from the relative sanity of C# code (the jump table is populated with OUT (n), A instructions which are subsequently trapped and handled by the emulator).

One thing I hadn't realised is that the graphics operations that BBC BASIC offers are actually implemented via the OSWRCH handler (OS WRite CHaracter), which means that BBC BASIC's PLOT, MOVE and DRAW commands will also be available, as well as any commands that use them indirectly (such as CIRCLE).

BBC BASIC

Monday, 19th May 2008

This is a project I initially attempted to get off the ground about four years ago, but never did. Anyhow, I've started work on it, and thanks to help from Richard Russell (the original developer) and J.G.Harston (who comparatively recently developed the Sinclair ZX Spectrum port) it looks like it should be possible this time around.

BBC BASIC was the native programming language on Acorn's BBC Micro. It's a structured BASIC dialect and supports procedures and functions, permitting far nicer code than the line-numbered GOTO and GOSUB code on other contemporary machines. It also has a built-in assembler, for inline assembly.

There is no source available, which is where the problems start to come in. Fortunately, J.G.Harston has developed a utility that permits the platform-agnostic BBC BASIC interpreter to be relocated. However, it assumes that the system has a jump table in RAM from $FF80..$FFFF (this jump table would be used to call platform-specific code); this memory range is not executable on the TI-83+. Execution protection in the $C000..$FFFF range may also cause issues for inline assembly code (which is, naturally, executed from RAM).

The TI-OS does not offer an especially suitable environment for BBC BASIC either; it is mainly menu driven (a command-line driven environment is preferable), does not have a plain text editor and does not use ASCII. To resolve this issues, I've concentrated on developing a suitable environment for BBC BASIC to live in, including a command-line interface and text editor.

Text files are stored as AppVars with a TEXTFILE header, and I've developed a Windows-based notepad clone for editing them (it saves and loads directly to and from .8xv). The following commands are currently supported (see here for a reference from the Windows verion): BYE, COPY, DELETE, DIR, ERASE, EXEC, QUIT, RENAME, TYPE, |.

To enter the editor, EDIT can be used. This presents a full-screen editor a little like the TI-OS program editor, but edits plain text files.

The interface transparently supports AT keyboards (which are rather easier to type on than the TI's keypad). The character resolution is 24 columns in 10 rows (4x6 pixel characters), giving you quite a lot of room to see what you're working on.

I intend on the final program being a 2-page Flash application; one page for BBC BASIC, and one page for the environment and OS interface. This unfortunately makes this a TI-83+ only project.

Even if I don't manage to shoe-horn BBC BASIC onto the TI-83+, the interface code (which uses direct hardware access for everything but opening and editing AppVars) could be useful for other projects.

CSG, fisheye and spotlights.

Monday, 5th May 2008

One way of constructing solids is to use a method named constructive solid geometry (or CSG for short). I added two simple CSG operators - intersection and subtraction - that both take two surfaces and return the result.

In the above image, the surface that makes up the ceiling is created by subtracting a sphere from a plane. Of course, much more interesting examples can be created. For example, here is the surface created by taking a sphere and subtracting three cylinders from it (each cylinder points directly along an axis).

One problem with the camera implementation was that it couldn't be rotated. To try and aid this, I used a spherical to cartesian conversion to generate the rays - which has the side-effect of images with "fisheye" distortion.

The above left image also demonstrates a small amount of refraction - something that I've not got working properly - through the surface. The above right image is the result of the intersection of three cylinders aligned along the x,y and z axes.

To try and combat the fisheye distortion, I hacked together a simple matrix structure that could be used to rotate the vectors generated by the earlier linear projection. The result looks a little less distorted!

The final addition to the raytracer before calling it a day was a spotlight. The spotlight has an origin, like the existing point light - but it adds a direction (in which it points) and an angle to specify how wide the beam is. In fact, there are two angles - if you're inside the inner one, you're fully lit; if you're outside the outer one, you're completely in the dark; if you're between the two then the light's intensity is blended accordingly.

In the above screenshot, a spotlight is shining down and backwards away from the camera towards a grid of spheres.

If you're interested in an extremely slow, buggy, and generally badly written raytracer, I've uploaded the C# 3 source and project file. The majority of the maths code has been pinched and hacked about from various sites on the internet, and there are no performance optimisations in place. I do not plan on taking this project any further.

Building and running the project will result in the above image, though you may well wish to put the kettle on and make yourself a cup of tea whilst it's working.

Cylinders and translucent surfaces

Tuesday, 29th April 2008

The first addition to the raytracer was a cylindrical surface, represented by two end points and a radius. In the two screenshots above, the cylinder is infinitely long - not very useful. However, by calculating the point on the cylinder's axis that is closest to the struck point on its surface you can work out how far along its axis you are, and from that whether you are between either of the cylinder's ends.

The cylinder can have its ends optionally capped. To add the caps, you can create plane that has a normal that points in the the direction of the cylinder's axis. If you collide with the plane, you can then calculate the distance between the point you struck on it and the end coordinate of the cylinder. If this distance is smaller than the radius of the cylinder, you've hit one of the end caps.

Texturing the cylinders proved rather difficult. The v component of the texture component can be calculated by working how far along the cylinder's axis you are - easy. However, to wrap a texture around the rotational axis of the cylinder is a bit more complicated. In the first screenshot, I simply used Math.Atan2(z,x) to get the angle, and hence texture coordinate - but this only works if the cylinder points along the y axis. If I had another vector that lay perpendicular to the cylinder's axis I could use the dot product to work out its angle, but I don't. The cross product could generate one, but I'd need another vector to cross the axis with... In the end, this post came to my rescue, and I managed to get it working for cylinders pointing along any axis - producing the second screenshot.

An addition I've wanted to make for a while was support for translucent surfaces.

This required a few changes to the structure of the raytracer. Previously, all methods for calculating ray intersections had to return a single Collision object, which contained a boolean flag specifying whether the collision was succesful. A translucent sphere would need to return two collision points - one as the ray enters the front and one as it leaves the back of its surface. To this end, all collision detection methods now return an array (empty or null if no collisions were made), and each collision has a flag indicating whether the collision was made by the ray entering the solid or leaving the solid (this is required, for example, to invert surface normals for correct shading).

Once the nearest struck point to the camera has been handled (including recursive reflection-handling code) it is checked to see if it's on a translucent surface. If so, the raytracer continues raytracing away from the camera, and blends the new result with the existing result based on its opacity. By stopping and starting again, one can adjust the direction of the ray - for example, to add a refraction effect (which I have not yet got working ).

One trick the above image misses is that it's still simply scaling down the intensity of the light by the opacity of the surface it passes through. It would look nicer if the light was coloured by the surface it passes through; so, in the above example, the white light shining through the blue water on the sphere should cast blue-tinted shadows.

Whilst it's far from being real-time, I can still make it dump out a sequence of frames to create a basic animation.

Fixed reflections and proper textures

Sunday, 27th April 2008

Just over a minute, so not very good performance at all. I've made some changes since then (including multithreading) that drop it down to about 30 seconds.

There is definitely something wrong with the reflections.

I decided to rewrite the main raycasting code from scratch, after seeing results such as the above. I'm not sure where the speckles were coming from, nor why the reflections were being calculated incorrectly. The new code writes to regions of an array of integers (for 32-bit ARGB output), and is designed much more simply. By splitting the output buffer into two halves I can perform the raytracing in two threads, which makes much better use of modern dual-core CPUs.

Before and after rewrite.

A scene with lots of reflective spheres would seem like a good test. If you look at the reflections in the outer ring of spheres, they're quite different (and now appear to be correct) now, so whatever was wrong now seems to have been fixed.

A similar scene to the one at the top of this entry.

A scene with multiple reflective planes no longer appears to have the noise and reflection bugs that were clearly visible in the first screenshot in this entry.

Textures would certainly make the objects look a bit more interesting, but I couldn't think of a simple way of aligning a texture to a surface. I decided that textures should be treated as simple 2D rectangles, and each material can now have a diffuse texture applied to it (which provides a method Colour GetColour(Vector2 coordinate) to read it). To attach the texture to the surface of an object the surface needs to implement ITexturable, which exposes the method Vector2 GetTextureCoordinate(Vector3 surfacePoint).

In short; it's the job of the surface class (such as the Sphere or Plane classes) to map the struck point to a texture coordinate. This is most easily handled with the sphere, which simply converts the cartesian coordinates of the stuck point to polar coordinates.

The small foreground sphere has an Earth texture.

For planes, I thought that the easiest way of aligning the texture would be to declare two vectors - one that represents the texture's X axis and one that represents the texture's Y axis.

For example, take the white wall at the back of the room in the above screenshot. To align a texture parallel to its surface, one could set the texture's X axis vector to point right and its Y axis vector to point down. By changing the magnitude of these vectors the texture can be scaled.

The back wall and floor are textured planes.

For the floor in the above image, the texture's X axis points right, and its Y axis points into the screen.

As the texture merely has to provide a method that takes in a texture coordinate and outputs a colour, this lets us declare simple procedural textures.

The floor and ceiling textures are procedurally generated.

The rather garish ceiling is declared like this in code:

this.Tracer.Objects.Add(new WorldObject() {
	Surface = new Plane(Vector3.Down, 10.0d) {
		TextureXAxis = Vector3.Right,
		TextureYAxis = Vector3.Forward,
	},
	Material = new Material() {
		Colour = Colour.White,
		Texture = new ProceduralTexture(
			p => new Colour(
				1.0d,
				(Math.Sin(p.X) * Math.Cos(p.Y * 2)) / 2.0d + 0.5d,
				(Math.Cos(p.X) * Math.Sin(p.Y * 3)) / 2.0d + 0.5d,
				(Math.Sin(p.X * 5) * Math.Sin(p.Y / 0.3d)) / 2.0d + 0.5d
			)
		),
	},
});

I think before I go any further I'm going to need to support a wider variety of surfaces than spheres and planes. Another limitation with the existing implementation is that only a single collision between a ray and a surface is reported, which limits what can be done with the renderer - for example, a glass sphere that refracts a ray that passes through it would need to report two collisions, one for the front of the sphere as the ray passes through and again one for the back as the ray leaves.