'
'   "Center.zen" solves for the center and radius
'   of a circle
'
'   Sample program for the Zeno Interpreter by:
'
'   Stephen R. Schmitt
'   962 Depot Road
'   Boxborough, MA 01719
'
OPTION base 1

TYPE POINT
 x AS float
 y AS float
END TYPE

' program

DIM r AS float
DIM c AS POINT
DIM p(3) AS POINT

p(1).x = 7
p(1).y = 7

p(2).x = 0
p(2).y = 8

p(3).x = 0
p(3).y = 0

PRINT "points: ";
PRINT "("; p(1).x; ","; p(1).y; "), ";
PRINT "("; p(2).x; ","; p(2).y; "), ";
PRINT "("; p(3).x; ","; p(3).y; ") "

r = circ( c, p() )
IF r > 0 THEN
 PRINT "Circle: ("; c.x; ","; c.y; "),"; r
ELSE
 PRINT "Not a circle!"
END IF

END

'
'  Calculate center and radius of
'  circle given three points
'
FUNCTION circ( c AS POINT, p() AS point) AS float

 LOCAL i AS integer
 LOCAL float r, m11, m12, m13, m14
 LOCAL a(3,3) AS float

 FOR i = 1 TO 3         ' find minor 11
   a(i,1) = p(i).x
   a(i,2) = p(i).y
   a(i,3) = 1
 NEXT i
 m11 = DET(a())

 FOR i = 1 TO 3         ' find minor 12
   a(i,1) = p(i).x^2 + p(i).y^2
   a(i,2) = p(i).y
   a(i,3) = 1
 NEXT i
 m12 = DET(a())

 FOR i = 1 TO 3         ' find minor 13
   a(i,1) = p(i).x^2 + p(i).y^2
   a(i,2) = p(i).x
   a(i,3) = 1
 NEXT i
 m13 = DET(a())

 FOR i = 1 TO 3         ' find minor 14
   a(i,1) = p(i).x^2 + p(i).y^2
   a(i,2) = p(i).x
   a(i,3) = p(i).y
 NEXT i
 m14 = DET(a())

 IF m11 = 0 THEN
   r = 0                ' not a circle
 ELSE
   c.x =  0.5 * m12 / m11 ' center of circle
   c.y = -0.5 * m13 / m11
   r   = SQR( c.x^2 + c.y^2 + m14/m11 )
 END IF

 circ = r               ' the radius

END FUNCTION

PicoMite MMBasic RP2350B V6.03.00
OPTION SERIAL CONSOLE COM1,GP0,GP1,BOTH
OPTION LCD SPI GP10,GP11,GP12
OPTION SYSTEM I2C GP6,GP7, SLOW
OPTION BAUDRATE 19200
OPTION FLASH SIZE 16777216
OPTION LIBRARY_FLASH_SIZE  4B000
OPTION COLOURCODE ON
OPTION CASE UPPER
OPTION TAB 8
OPTION DEFAULT COLOURS GREEN, BLACK
OPTION KEYBOARD PICOCALC
OPTION PICO OFF
OPTION CPUSPEED (KHz) 384000
OPTION LCDPANEL CONSOLE ,, FF00
OPTION DISPLAY 26, 40
OPTION LCDPANEL ST7365P, PORTRAIT,GP14,GP15,GP13
OPTION BACKLIGHT LCD 80
OPTION GUI CONTROLS 50
OPTION SDCARD GP17, GP18, GP19, GP16
OPTION AUDIO GP26,GP27', ON PWM CHANNEL 5
OPTION RTC AUTO ENABLE
OPTION MODBUFF ENABLE  192
OPTION PLATFORM PicoCalc
OPTION PSRAM PIN GP47

FUNCTION DET(n())
 DET=MATH(m_determinant n())
END FUNCTION

a()=INV(b())  ' Like MAT A = INV(B) in standard BASIC
c()=TRN(r())  ' Like MAT C = TRN(R) in standard BASIC

FUNCTION INV(n())
 LOCAL m(BOUND(n(),1), BOUND(n(),2))
 MATH M_INVERSE n(), m()
 INV=m()
END FUNCTION

FUNCTION TRN(n())
 LOCAL m(BOUND(n(),1), BOUND(n(),2))
 MATH M_TRANSPOSE n(), m()
 TRN=m()
END FUNCTION