Spectrum ROM: Routine at 08992

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	08992	RST 24	Get the present character.
	08993	CP ","	Test for comma.
	08995	JP NZ,REPORT_C	If not so, report the error.
	08998	RST 32	Get next character (the radius).
	08999	CALL CLASS_06	Radius to calculator stack.
	09002	CALL CHECK_END	Move to consider next statement if checking syntax.
	09005	RST 40	Use calculator.
	09006	DEFB 42	abs: X, Y, Z
	09007	DEFB 61	re_stack: Z is re-stacked; its exponent is therefore available.
	09008	DEFB 56	end_calc
	09009	LD A,(HL)	Get exponent of radius.
	09010	CP 129	Test whether radius less than 1.
	09012	JR NC,C_R_GRE_1	If not, jump.
	09014	RST 40	If less, delete it from the stack.
	09015	DEFB 2	delete: X, Y
	09016	DEFB 56	end_calc
	09017	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	09019	RST 40
	09020	DEFB 163	stk_pi_2: X, Y, Z, π/2
	09021	DEFB 56	end_calc
	09022	LD (HL),131	Now increase exponent to 131, changing π/2 into 2π.
	09024	RST 40	X, Y, Z, 2π.
	09025	DEFB 197	st_mem_5: (2π is copied to mem-5)
	09026	DEFB 2	delete: X, Y, Z
	09027	DEFB 56	end_calc
	09028	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.
	09031	PUSH BC	Save the arc-count in B.
	09032	RST 40	X, Y, Z
	09033	DEFB 49	duplicate: X, Y, Z, Z
	09034	DEFB 225	get_mem_1: X, Y, Z, Z, SIN (π/A)
	09035	DEFB 4	multiply: X, Y, Z, Z*SIN (π/A)
	09036	DEFB 56	end_calc
	09037	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.
	09038	CP 128
	09040	JR NC,C_ARC_GE1	If not, the jump is made.
	09042	RST 40
	09043	DEFB 2	delete: X, Y, Z
	09044	DEFB 2	delete: X, Y
	09045	DEFB 56	end_calc
	09046	POP BC	Clear the machine stack.
	09047	JP PLOT	Jump to plot X, Y.
C_ARC_GE1	09050	RST 40	X, Y, Z, Z*SIN (π/A)
	09051	DEFB 194	st_mem_2: (Z*SIN (π/A) to mem-2 for now)
	09052	DEFB 1	exchange: X, Y, Z*SIN (π/A), Z
	09053	DEFB 192	st_mem_0: X, Y, Z*SIN (π/A), Z (Z is copied to mem-0)
	09054	DEFB 2	delete: X, Y, Z*SIN (π/A)
	09055	DEFB 3	subtract: X, Y-Z*SIN (π/A)
	09056	DEFB 1	exchange: Y-Z*SIN (π/A), X
	09057	DEFB 224	get_mem_0: Y-Z*SIN (π/A), X, Z
	09058	DEFB 15	addition: Y-Z*SIN (π/A), X+Z
	09059	DEFB 192	st_mem_0: (X+Z is copied to mem-0)
	09060	DEFB 1	exchange: X+Z, Y-Z*SIN (π/A)
	09061	DEFB 49	duplicate: X+Z, Y-ZSIN (π/A), Y-ZSIN (π/A)
	09062	DEFB 224	get_mem_0: sa, sb, sb, sa
	09063	DEFB 1	exchange: sa, sb, sa, sb
	09064	DEFB 49	duplicate: sa, sb, sa, sb, sb
	09065	DEFB 224	get_mem_0: sa, sb, sa, sb, sb, sa
	09066	DEFB 160	stk_zero: sa, sb, sa, sb, sb, sa, 0
	09067	DEFB 193	st_mem_1: (mem-1 is set to zero)
	09068	DEFB 2	delete: sa, sb, sa, sb, sb, sa
	09069	DEFB 56	end_calc
(Here sa denotes X+Z and sb denotes Y-Z*SIN (π/A).)
	09070	INC (IY+98)	Incrementing the exponent byte of mem-2 sets mem-2 to 2ZSIN(π/A).
	09073	CALL FIND_INT1	The last value X+Z is moved from the stack to A and copied to L.
	09076	LD L,A
	09077	PUSH HL	It is saved in HL.
	09078	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.
	09081	POP HL
	09082	LD H,A
	09083	LD (23677),HL	It is copied to COORDS.
	09086	POP BC	The arc-count is restored.
	09087	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.)