2D Graphics
John E. Laird Based on Tricks of the GameProgramming Gurus pp.72-109 Lots of obvious observations that make drawing easy
Vector Graphics
Directly control electronic gun of CRT
Drawings defined as lines Lines stored as endpoints Look like wireframes No curved lines Limited variation in color or intensity.
History of 2D graphics: Vector
Example: Asteroids, Battlezone
http://www.squadron13.com/games/asteroids/asteroids.htm
Advantages:
Control the electronic gun directly so can be fast Only draw what is on the screen No jagged lines (aliasing). Only store endpoints of lines
Problems:
Best for wireframes. Must draw everything as lines: text, circles, surfaces, ... $$s: Cant use commercial TV technology
Example Displays:
Textronics, GDP
Raster Graphics
Advantages:
Cheaper Can easily draw solid surfaces Maps screen onto 2D memory Can move blocks of image around, control individual pixels
Problems:
Memory intensive Aliasing problems
Example:
VGA =
640 x 350 with 16 colors 320x200 with 256 colors
Raster Graphics
Screen is made up of picture elements = pixels. Color defined by mixture of 3-guns: Red, Green, Blue
Current Approach
Use Raster Graphics as underlying technology
Memory is cheap Get access is every point on the screen
Create drawing primitives similar to those in vector graphics
Drawing lines
Support surfaces, textures, sprites, fonts, etc. directly Sprites vs. Graphics??
2D Graphics
Points
x,y
4,4
Lines
Two points Draw by drawing all points in between Low-level support for this in hardware or software
-2,-1
Coordinate System
(0,0) +x
(120,120)
+y
Polygons
Defined by vertices Closed: all lines connected Draw one line at a time Can be concave or convex Basis for many games Required data:
Number of vertices Color Position: x, y List of vertices
Might be array with reasonable max
100,100
moveto(100,100) lineto(100,300) lineto(500,300) lineto(500,100) lineto(100,100)
Positioning an object
Problem: If we move an object, do we need to change the values of every vertex? Solution:
World coordinate system for objects
coordinates relative to screen
Local coordinate system for points in object
coordinates relative to the position of the object
P1
Triangle location: 4,0
P1: 0, 1 P2: -1, -1 P3: 1, -1
P2
P3
Translation: Moving an Object
To move an object, just add in changes to position:
xo = xo + dx yo = yo + dy
If have motion, the dx and dy are the x and y components of the velocity vector.
dy = sin v
Velocity Vector: V
dx = cos v
x0, y0
Scaling: Changing Size
Multiply the coordinates of each vertex by the scaling factor. Everything just expands from the center.
object[v1].x = object[v1].x * scale object[v1].y = object[v1].y * scale
Rotation: Turning an object
Spin object around its center in the z-axis. Rotate each point the same angle
Positive angles are clockwise Negative angles are counterclockwise new_x = x * cos(angle) - y * sin(angle) new_y = y * cos(angle) + x * sin(angle)
Remember, C++ uses radians not degrees!
Matrix Operations
Translation, rotation, scaling can all be collapsed into matrix operations:
1 0 1 0 0 1 0 0 1 0 0 1
Translation:
dx dy sx 0
Scaling:
sx, sy = scaling values
0 0
sy 0
cos -sin
Rotation:
sin 0
cos 0
Putting it all together
sx*cos sy*sin dx -sx*sin sy*cos dy 0 0 1
Common Problems: Flicker
Too slow updating Change video buffer during updating. Solution:
Double buffering -- write to a virtual screen that isnt being displayed. Either BLT buffer all at once, or switch pointer. Video Pointer
Video Buffer
Backup Buffer
Speed Issues (Gone)
Using regular drawing routines
Original Microsoft graphics library (GDI) was quite slow Not a problem now DirectX is ok
Using Floating Point
Floating point used to be much slower than integer Not a problem with Pentium architecture
Using Standard Trig functions
Current machines are fast enough If you start having performance problems, pre-compute and store all rotations you are going to need
Image Space vs. Object Space
Image space:
What is going to be displayed Primitives are pixels Operations related to number of pixels
Bad when must to in software Good if can do in parallel in hardware have one processor/pixel
Object space:
Objects being simulated in games Primitives are objects or polygons Operations related to number of objects
Clipping
Display the parts of the objects on the screen.
Can get array errors, etc. if not careful. Easy for sprites done in DirectX
Approaches:
Border vs. image space or object space
Border Clipping
Create a border that is as wide as widest object
Only render image Restricted to screen/rectangle clipping Still have to detect when object is all gone Requires significantly more memory
Image Space Clipping
Image Space:
The pixel-level representation of the complete image.
Clipping
For each point, test if it is in the region that can be drawn before trying to draw it If buffer is 320x200, test 0-319 in x, 0-199 in y.
Evaluation
Easy to implement Works for all objects: lines, pixels, squares, bit maps Works for subregions Expensive! Requires overhead for every point rendered if done in software. Cheap if done in hardware (well the hardware cost something).
Object Space Clipping
Object space:
Representation of lines, polygons, etc.
Clipping
Change object to one that doesnt need to be clipped New object is passed to render engine without any testing for clipping
Evaluation
Usually more efficient than image space software
But hardware support of image space is fast
Need different algorithm for different types of objects
Lines are easy. Concave objects are problematic Usually just worry about bitmaps
Line Clipping Cases
4 1
Collision Detection
Image Space:
Pixel by pixel basis. Expensive.
Object Space:
Hard for complex and concave spaces:
Standard Approach:
Cheat! Create a bounding box or circle
test each vertex to see in another object
Hide this by making your objects boxy Dont have objects like:
Scrolling - simple
screen
Scrolling Tile Based
Tile map
screen
Scrolling Sparse
Object-based
Keep list of objects with their positions Each time render those objects in current view Go through list of object linear in # of objects
Grid-based
Overlay grid with each cell having a list of objects Only consider objects in cells that are in view
