Spectrum ROM: Routine at 2320

The address of this routine is found in the parameter table.

This routine draws an approximation to the circle with centre co-ordinates X and Y and radius Z. These numbers are rounded to the nearest integer before use. Thus Z must be less than 87.5, even when (X,Y) is in the centre of the screen. The method used is to draw a series of arcs approximated by straight lines.

CIRCLE has four parts:

i. Tests the radius. If its modulus is less than 1, just plot X,Y.
ii. Calls CD_PRMS1, which is used to set the initial parameters for both CIRCLE and DRAW.
iii. Sets up the remaining parameters for CIRCLE, including the initial displacement for the first 'arc' (a straight line in fact).
iv. Jumps to DRW_STEPS to use the arc-drawing loop.

Parts i. to iii. will now be explained in turn.

i. The radius, say Z', is obtained from the calculator stack. Its modulus Z is formed and used from now on. If Z is less than 1, it is deleted from the stack and the point X,Y is plotted by a jump to PLOT.

The address of this routine is found in the parameter table. This routine draws an approximation to the circle with centre co-ordinates X and Y and radius Z. These numbers are rounded to the nearest integer before use. Thus Z must be less than 87.5, even when (X,Y) is in the centre of the screen. The method used is to draw a series of arcs approximated by straight lines. CIRCLE has four parts: i. Tests the radius. If its modulus is less than 1, just plot X,Y. ii. Calls CD_PRMS1, which is used to set the initial parameters for both CIRCLE and DRAW. iii. Sets up the remaining parameters for CIRCLE, including the initial displacement for the first 'arc' (a straight line in fact). iv. Jumps to DRW_STEPS to use the arc-drawing loop. Parts i. to iii. will now be explained in turn. i. The radius, say Z', is obtained from the calculator stack. Its modulus Z is formed and used from now on. If Z is less than 1, it is deleted from the stack and the point X,Y is plotted by a jump to PLOT.
CIRCLE	2320	RST $18	Get the present character.
	2321	CP ","	Test for comma.
	2323	JP NZ,REPORT_C	If not so, report the error.
	2326	RST $20	Get next character (the radius).
	2327	CALL CLASS_06	Radius to calculator stack.
	232A	CALL CHECK_END	Move to consider next statement if checking syntax.
	232D	RST $28	Use calculator.
	232E	DEFB $2A	abs: X, Y, Z
	232F	DEFB $3D	re_stack: Z is re-stacked; its exponent is therefore available.
	2330	DEFB $38	end_calc
	2331	LD A,(HL)	Get exponent of radius.
	2332	CP $81	Test whether radius less than 1.
	2334	JR NC,C_R_GRE_1	If not, jump.
	2336	RST $28	If less, delete it from the stack.
	2337	DEFB $02	delete: X, Y
	2338	DEFB $38	end_calc
	2339	JR PLOT	Just plot the point X, Y.
ii. 2π is stored in mem-5 and CD_PRMS1 is called. This subroutine stores in the B register the number of arcs required for the circle, viz. A=4INT (πSQR Z/4)+4, hence 4, 8, 12, etc., up to a maximum of 32. It also stores in mem-0 to mem-4 the quantities 2π/A, SIN(π/A), 0, COS (2π/A) and SIN (2π/A).
C_R_GRE_1	233B	RST $28
	233C	DEFB $A3	stk_pi_2: X, Y, Z, π/2
	233D	DEFB $38	end_calc
	233E	LD (HL),$83	Now increase exponent to +83, changing π/2 into 2π.
	2340	RST $28	X, Y, Z, 2π.
	2341	DEFB $C5	st_mem_5: (2π is copied to mem-5)
	2342	DEFB $02	delete: X, Y, Z
	2343	DEFB $38	end_calc
	2344	CALL CD_PRMS1	Set the initial parameters.
iii. A test is made to see whether the initial 'arc' length is less than 1. If it is, a jump is made simply to plot X, Y. Otherwise, the parameters are set: X+Z and X-ZSIN (π/A) are stacked twice as start and end point, and copied to COORDS as well; zero and 2ZSIN (π/A) are stored in mem-1 and mem-2 as initial increments, giving as first 'arc' the vertical straight line joining X+Z, y-ZSIN (π/A) and X+Z, Y+ZSIN (π/A). The arc-drawing loop at DRW_STEPS will ensure that all subsequent points remain on the same circle as these two points, with incremental angle 2π/A. But it is clear that these 2 points in fact subtend this angle at the point X+Z(1-COS (π/A)), Y not at X, Y. Hence the end points of each arc of the circle are displaced right by an amount 2*(1-COS (π/A)), which is less than half a pixel, and rounds to one pixel at most.
	2347	PUSH BC	Save the arc-count in B.
	2348	RST $28	X, Y, Z
	2349	DEFB $31	duplicate: X, Y, Z, Z
	234A	DEFB $E1	get_mem_1: X, Y, Z, Z, SIN (π/A)
	234B	DEFB $04	multiply: X, Y, Z, Z*SIN (π/A)
	234C	DEFB $38	end_calc
	234D	LD A,(HL)	Z*SIN (π/A) is half the initial 'arc' length; it is tested to see whether it is less than 0.5.
	234E	CP $80
	2350	JR NC,C_ARC_GE1	If not, the jump is made.
	2352	RST $28
	2353	DEFB $02	delete: X, Y, Z
	2354	DEFB $02	delete: X, Y
	2355	DEFB $38	end_calc
	2356	POP BC	Clear the machine stack.
	2357	JP PLOT	Jump to plot X, Y.
C_ARC_GE1	235A	RST $28	X, Y, Z, Z*SIN (π/A)
	235B	DEFB $C2	st_mem_2: (Z*SIN (π/A) to mem-2 for now)
	235C	DEFB $01	exchange: X, Y, Z*SIN (π/A), Z
	235D	DEFB $C0	st_mem_0: X, Y, Z*SIN (π/A), Z (Z is copied to mem-0)
	235E	DEFB $02	delete: X, Y, Z*SIN (π/A)
	235F	DEFB $03	subtract: X, Y-Z*SIN (π/A)
	2360	DEFB $01	exchange: Y-Z*SIN (π/A), X
	2361	DEFB $E0	get_mem_0: Y-Z*SIN (π/A), X, Z
	2362	DEFB $0F	addition: Y-Z*SIN (π/A), X+Z
	2363	DEFB $C0	st_mem_0: (X+Z is copied to mem-0)
	2364	DEFB $01	exchange: X+Z, Y-Z*SIN (π/A)
	2365	DEFB $31	duplicate: X+Z, Y-ZSIN (π/A), Y-ZSIN (π/A)
	2366	DEFB $E0	get_mem_0: sa, sb, sb, sa
	2367	DEFB $01	exchange: sa, sb, sa, sb
	2368	DEFB $31	duplicate: sa, sb, sa, sb, sb
	2369	DEFB $E0	get_mem_0: sa, sb, sa, sb, sb, sa
	236A	DEFB $A0	stk_zero: sa, sb, sa, sb, sb, sa, 0
	236B	DEFB $C1	st_mem_1: (mem-1 is set to zero)
	236C	DEFB $02	delete: sa, sb, sa, sb, sb, sa
	236D	DEFB $38	end_calc
(Here sa denotes X+Z and sb denotes Y-Z*SIN (π/A).)
	236E	INC (IY+$62)	Incrementing the exponent byte of mem-2 sets mem-2 to 2ZSIN(π/A).
	2371	CALL FIND_INT1	The last value X+Z is moved from the stack to A and copied to L.
	2374	LD L,A
	2375	PUSH HL	It is saved in HL.
	2376	CALL FIND_INT1	Y-Z*SIN (π/A) goes from the stack to A and is copied to H. HL now holds the initial point.
	2379	POP HL
	237A	LD H,A
	237B	LD ($5C7D),HL	It is copied to COORDS.
	237E	POP BC	The arc-count is restored.
	237F	JP DRW_STEPS	The jump is made to DRW_STEPS.
(The stack now holds X+Z, Y-ZSIN (π/A), Y-ZSIN (π/A), X+Z.)