2.5 Games

• Def. Also called pseudo-3D, they are games that appear to be 3 dimensional, but without having 3D freedom of movement.
• Usually the world is 2D but the game tokens are drawn in the 3rd dimension.
• The rendering uses a fixes projection, usually parallel.

Age of Empires example

Examples

• Age of Empires
• Sim City
• Arcanum
• Diablo 1 and 2
• Roller Coaster Tycoon 1 and 2
• Mega Man Battle Network
• Super Mario RPG
• Starcraft

Technical Details

• Many of these games render objects with a bitmap/texture applied to a simple polygon.
• Since the image used is display in a plane perpendicular to the view direction, it is called billboarding.
• If your projection never changes through the game, you can work directly with the projected coordinates.

Simplest Projection

• The scene is in 2D (x and y), but each object has a z (depth) property attached to it.
• To solve the issue of overlapping objects, they are drawn in reverse order of their z coordinate.

Axonometric Projection

• Axonometric projection - popular in architecture. It means that the 3 axes are equally distorted. Related: dimetric (2 axes are equally distorted), trimetric.
• All the lines parallel to the x and z axes are parallel and kept in proportion.
• Start with a 2D plan of the area. Draw each object up at a fixed angle (45^o).
• It usually consists of a rotation around y followed by a rotation around x. It can be accompanied by a scaling over z to simulate perspective.
• It can be rendered using simple formulas.

Isometric projection and angles.

Axonometric projections and used angles.

Example

• Let P(x, 0, z) be the object to draw. Then the projection on the screen will be defined by
• x_d = x cos a + z sin a
• z_d = -x sin a + z cos a
• y_d = c z_d
• Sort the objects by z_d and draw them in reverse order at position (x_d, y_d) on the screen.