4. Shapes and Patterns
Important Note: All variables in degrees must be converted to RADians as BASIC can only interpret radians.
Changing the Geometry
Simply adding additional geometric shapes to the basic shapes discussed previously can make the graphic more dynamic and interesting. One of the simplest to enhance is the circle.
Circles
The circle is the basis for an elementary graphic. Adding additional circles with their centres equi-spaced around the circumference of a central circle gives a simple but effective graphic and uses BASICs trigonometrical functions, sine and cosine to find the centres of the outside circles (figure 6).
Fig 6: Multi-circles
Start with a simple circle:
MODE 1920,1080,32
ORIGIN 1920,1080
r = 500
CIRCLE 0,0,r
Now add the other 6 circles:
MODE 1920,1080,32
ORIGIN 1920,1080
r = 500
CIRCLE 0,0,r
FOR circ = 0 TO 300 STEP 60
CIRCLE r*COS RAD(circ),r*SIN RAD(circ),r
NEXT
Ellipse
A simple ellipse pattern can be created to give a pseudo torus. It starts with a basic ellipse drawn in the horizontal position (figure 7).
Fig 7 Simple ellipse
Simply adding a FOR-NEXT loop to change the angle from 0 to PI (180°) and a STEP size of 0.15 gives the picture shown (figure 9). The STEP variable is critical to ensure the distance between each ellipse is the same. It gives 20 rotated ellipses + the base ellipse = 21 in total. A STEP size of 0.14 or 0.16 draws an incorrect gap size for the last ellipse.
Fig 9 Pseudo torus
REM Create a pseudo torus
MODE 1920,1080,32 : OFF
X=1000 : Y=500
FOR angle=0 TO PI STEP 0.15
ELLIPSE 1920,1080,X,Y,angle
NEXT
Ellipses at 90 Degrees
Overlapping ellipses as shown in figure 10 can be created with the routine below
Fig 10 Ellipses at 90° (only 6 pairs of ellipses are shown)
MODE 1920,1080,32 : OFF
ORIGIN 1920,1080
GCOL ON 255,255,200 : CLG
X=100 : Y=50
REPEAT
ELLIPSE 0,0,X,Y, PI/2 : REM Vertical ellipse
GCOL OF RND(255),RND(255),RND(255)
ELLIPSE 0,0,X,Y : REM Horizontal ellipse
X+=50 : Y+=50
UNTIL X=1050
Polygons
There are several ways of creating polygons for example to draw a hexagon requires a minimum of code as shown:
MODE 1920,1080,32 : OFF
X = 1920 : Y = 1080 : R = 1000
MOVE X + R, Y : REM Move to first point
FOR theta = 0 TO 360 STEP 60
DRAW X+R*COS(RAD(theta)),Y+R*SIN(RAD(theta))
NEXT theta
Note: Program uses degrees in the FOR-NEXT loop but converted to RADians in the DRAW command.
Just change the STEP size to alter the number of sides (eg. STEP 45 will create an octagon).
An extension to the hexagon program draws many polygons in a concentric pattern, starting with a square and finishing with a dodecagon:
MODE 1920,1080,32 : OFF
X = 1920 : Y = 1080
FOR sides = 4 TO 12
radius = 80*sides
PROCPOLY
NEXT sides
END
DEF PROCPOLY
MOVE X+radius,Y
D_theta = 2 * PI/sides
theta=0
FOR N = 1 TO sides
theta=theta+D_theta
DRAW X+radius*COS(theta),Y+radius*SIN(theta)
NEXT N
ENDPROC
Star (Radial)
MODE 1920,1080,32
REM R=radius and NR the # of radials
PROCradials(1920,1080,1000,80)
END
DEF PROCradials(X,Y,R,NR)
theta=2*PI/NR
DX=R:DY=0
FOR N=1 TO NR
MOVE X,Y
DRAW X+DX,Y+DY
X1=DX*COS(theta)-DY*SIN(theta)
DY=DX*SIN(theta)+DY*COS(theta)
DX=X1
NEXT N
ENDPROC