Draw a sight line, a circular scanner or a filled oval without building a renderer first. These are five callable assembly routines over the existing pixel/span interface. You choose the bitmap, own the memory and call only the pieces your game needs.
Include it and make a call
The caller places BP at $0380 and G at $0400, outside the $0600–$1DFF bitmap. Scanlines are linear: address=$0600+y*32+(x div 8). The complete caller configures the SAM and PIA for this exact PMODE 4 display. Do not reuse that setup blindly on a different Dragon/CoCo mode.
Define GEO_WIDTH and GEO_HEIGHT as 256 and 192. Set GEO_PEN_MAX to 255 (pen ignored). Include the geometry 6809.inc and the backend exactly once, as shown at the bottom of the complete caller. Reserve 160 bytes at G plus 48 at BP, separately from code, stack, tables and display. Scratch needs no initialisation; public inputs do.
After the caller’s video setup, this is an ordinary direct call. Your game does not need the verification mailbox that follows it.
Outline an ellipse centred at (80,70), radii (48,24)
demo.asm, excerpt
; A normal game call: an outlined ellipse. Setup and mailbox are separate.
ldd #$0050
std G+0
ldd #$0046
std G+2
ldd #$0030
std G+4
ldd #$0018
std G+6
ldd #$0000
std G+12
ldd #$0000
std G+14
ldd #$0100
std G+16
ldd #$00c0
std G+18
lda #0
sta G+8
lda #0
sta G+9
lda #1
sta G+11
jsr geo_ellipse
lda #0
sta COMMAND
lda #239
sta COMMAND+1Read G+10 after return: 1 means accepted, 0 means rejected. An accepted shape can be completely outside the scissor and draw nothing. Change the inputs and call again; G holds no hidden scene or list of shapes.
The calling contract
All words use big-endian byte order. Screen origin is top left; Y increases downwards. Pen is ignored by this monochrome backend; initialise it to 1 for a caller that also ports to CPC.
| G offset | Supply or read |
|---|---|
| 0,2 | Signed x0,y0 for a line; centre cx,cy for curves |
| 4,6 | Signed x1,y1 for a line; radii rx,ry for an ellipse; a circle uses rx and ignores ry |
| 8 | Operation: 0 set/replace, 1 clear, 2 XOR |
| 9 | Line: 0 includes both ends, 1 omits the original caller’s final end; curves require 0 |
| 10 | Output: 1 accepted, 0 rejected |
| 11 | Pen index (ignored on mono backends) |
| 12,14,16,18 | Unsigned scissor left,top,right,bottom; right/bottom exclusive |
| 20 | Output: 32-bit destination-byte writes |
| 24 | Output: 16-bit backend calls |
| 26–159 | Private scratch |
Call geo_line, geo_circle, geo_ellipse, geo_fill_circle or geo_fill_ellipse. Coordinates must be −512..511, radii 0..255. The scissor must be nonempty and inside the 256×192 display. Invalid bounds, radii, operation, flags or pen reject before any destination write, with zero counters. Inputs at 0–9 and 11–19 survive. Unused circle ry is ignored. A zero radius becomes a point or straight span rather than an error.
Keep the line you asked for
The line uses accumulated integer error in all eight octants. It orders endpoints consistently before choosing half-way pixels, so reversing a line produces the same pixels. A horizontal or vertical line uses a span fast path. A zero-length inclusive line draws one pixel.
For a closed XOR polyline, give every edge flag 1. Each omits its original final endpoint, so the next edge owns that shared vertex. Leaving both endpoints on both edges would toggle the vertex twice and erase it. A zero-length omit-final line draws nothing.
The scissor discards outside pixels from the original raster, preserving its rounding phase. It does not replace the endpoints with rounded intersections. Offscreen steps still cost work: the accepted coordinate range bounds the major-axis delta at 1023. Filled curves instead intersect each row span with the scissor before calling the backend.
Draw with integer error works through a short line, symmetry, span filling and overflow. Place a point explains the origin difference; for integer screen rows here, convert an upwards world Y with screenY=height-1-worldY.
Fill rows, not thousands of point calls
Outline ellipses update an integer decision and reflect points into four quadrants. Axis points are emitted once. Filled ellipses select the widest interval for each row and emit that span once; they do not repeatedly XOR the same row as the edge advances. Circles use equal ellipse radii through this same kernel. A specialised eight-way circle implementation could reduce work further.
An ellipse with radii (37,15) covers 1,833 logical pixels here but needs only 31 span calls when filled. Those calls made 258 byte writes on this backend. That is actual destination work, not elapsed cycles. Four-pixel CPC packing and eight-pixel mono packing produce different counts, and partial edge bytes still need protection.
The geometry occupies 4,573 assembled bytes, the backend 470, plus the 208 RAM bytes for G and BP. Reset code, stack, display and assets are additional. The checked 32-bit curve arithmetic buys a clear range contract but has a code/time cost. Cache static shapes or specialise a hot path when measurement shows a need. No frame-budget claim has been measured here.
A logical circle has equal X/Y radii. Its displayed shape still depends on the display mode, pixel aspect and capture presentation. Choose the presentation deliberately; changing radius to compensate is a separate mapping decision, not a change to the circle equation.
Own the resources
Clobbered: D/X/Y/CC; U and DP survive. Reserve a conservative 64-byte stack budget, plus your other calls and interrupts. The component is non-re-entrant. It does not change interrupt state or negotiate display access. Keep G/BP private and coordinate another renderer or interrupt user yourself. Reset fixtures own the machine; integration under a live OS needs its own loading and coexistence checks.
Open the complete reusable 6809 geometry include
Include this CPU component once
6809.inc
; SPDX-License-Identifier: MIT
; Copyright (c) 2020 zingl; assembly adaptation Code198x (2026).
; Integer geometry over the existing bp_pixel/bp_hspan/bp_vspan backend.
; G is 160 caller-owned RAM bytes. BP is a separate 48-byte workspace.
; Read README.md for signed inputs, scissor, endpoint flags and ownership.
; Bresenham/ellipse recurrences adapted from Alois Zingl; see LICENSE-Zingl.txt.
g_a equ G+0
g_b equ G+2
g_c equ G+4
g_d equ G+6
g_op equ G+8
g_flags equ G+9
g_status equ G+10
g_pen equ G+11
g_clip_l equ G+12
g_clip_t equ G+14
g_clip_r equ G+16
g_clip_b equ G+18
g_writes equ G+20
g_calls equ G+24
g_mode equ G+32
g_first equ G+33
g_swap equ G+34
g_fill equ G+35
g_x equ G+40
g_y equ G+42
g_end_x equ G+44
g_end_y equ G+46
g_dx equ G+48
g_dy equ G+50
g_sy equ G+54
g_err equ G+56
g_e2 equ G+58
g_temp equ G+60
g_last_y equ G+62
g_rx equ G+64
g_ry equ G+66
g_px equ G+68
g_py equ G+70
g_right equ G+72
g_bottom equ G+74
g_a2 equ G+80
g_b2 equ G+84
g_curve_dx equ G+88
g_curve_dy equ G+92
g_curve_err equ G+96
g_curve_e2 equ G+100
g_step_x equ G+104
g_step_y equ G+108
g_work equ G+112
g_mul equ G+158
g_cmp equ G+159
bp_writes equ BP+40
bp_status equ BP+9
bp_op equ BP+8
bp_pen equ BP+11
bp_x0 equ BP+0
bp_y0 equ BP+2
bp_x1 equ BP+4
bp_y1 equ BP+6
geo_line
lda #$00
sta g_mode
jmp geo_enter
geo_circle
lda #$01
sta g_mode
jmp geo_enter
geo_ellipse
lda #$02
sta g_mode
jmp geo_enter
geo_fill_circle
lda #$03
sta g_mode
jmp geo_enter
geo_fill_ellipse
lda #$04
sta g_mode
jmp geo_enter
geo_enter
lda #$00
sta g_status
lda #$00
sta g_writes+3
lda #$00
sta g_writes+2
lda #$00
sta g_writes+1
lda #$00
sta g_writes
ldd #$0000
std g_calls
; Validate the entire request before the first backend write.
lda #$02
sta g_cmp
lda g_op
cmpa g_cmp
lblo geo_branch_1
lbne geo_done
geo_branch_1
lda g_pen
cmpa #GEO_PEN_MAX
lblo geo_branch_2
lbeq geo_branch_2
jmp geo_done
geo_branch_2
lda #$fe
eora #$80
sta g_cmp
lda g_a
eora #$80
cmpa g_cmp
lblo geo_done
lbne geo_branch_3
lda #$00
sta g_cmp
lda g_a+1
cmpa g_cmp
lblo geo_done
geo_branch_3
lda #$01
eora #$80
sta g_cmp
lda g_a
eora #$80
cmpa g_cmp
lblo geo_branch_4
lbne geo_done
lda #$ff
sta g_cmp
lda g_a+1
cmpa g_cmp
lblo geo_branch_4
lbne geo_done
geo_branch_4
lda #$fe
eora #$80
sta g_cmp
lda g_b
eora #$80
cmpa g_cmp
lblo geo_done
lbne geo_branch_5
lda #$00
sta g_cmp
lda g_b+1
cmpa g_cmp
lblo geo_done
geo_branch_5
lda #$01
eora #$80
sta g_cmp
lda g_b
eora #$80
cmpa g_cmp
lblo geo_branch_6
lbne geo_done
lda #$ff
sta g_cmp
lda g_b+1
cmpa g_cmp
lblo geo_branch_6
lbne geo_done
geo_branch_6
lda #$00
eora #$80
sta g_cmp
lda g_clip_l
eora #$80
cmpa g_cmp
lblo geo_done
lbne geo_branch_7
lda #$00
sta g_cmp
lda g_clip_l+1
cmpa g_cmp
lblo geo_done
geo_branch_7
lda #$00
eora #$80
sta g_cmp
lda g_clip_t
eora #$80
cmpa g_cmp
lblo geo_done
lbne geo_branch_8
lda #$00
sta g_cmp
lda g_clip_t+1
cmpa g_cmp
lblo geo_done
geo_branch_8
lda g_clip_r
eora #$80
sta g_cmp
lda g_clip_l
eora #$80
cmpa g_cmp
lblo geo_branch_9
lbne geo_done
lda g_clip_r+1
sta g_cmp
lda g_clip_l+1
cmpa g_cmp
lblo geo_branch_9
jmp geo_done
geo_branch_9
lda g_clip_b
eora #$80
sta g_cmp
lda g_clip_t
eora #$80
cmpa g_cmp
lblo geo_branch_10
lbne geo_done
lda g_clip_b+1
sta g_cmp
lda g_clip_t+1
cmpa g_cmp
lblo geo_branch_10
jmp geo_done
geo_branch_10
ldd #GEO_WIDTH
std g_temp
lda g_temp
eora #$80
sta g_cmp
lda g_clip_r
eora #$80
cmpa g_cmp
lblo geo_branch_11
lbne geo_done
lda g_temp+1
sta g_cmp
lda g_clip_r+1
cmpa g_cmp
lblo geo_branch_11
lbne geo_done
geo_branch_11
ldd #GEO_HEIGHT
std g_temp
lda g_temp
eora #$80
sta g_cmp
lda g_clip_b
eora #$80
cmpa g_cmp
lblo geo_branch_12
lbne geo_done
lda g_temp+1
sta g_cmp
lda g_clip_b+1
cmpa g_cmp
lblo geo_branch_12
lbne geo_done
geo_branch_12
lda #$00
sta g_cmp
lda g_mode
cmpa g_cmp
lbne geo_curve_validate
geo_branch_13
lda #$01
sta g_cmp
lda g_flags
cmpa g_cmp
lblo geo_branch_14
lbne geo_done
geo_branch_14
lda #$fe
eora #$80
sta g_cmp
lda g_c
eora #$80
cmpa g_cmp
lblo geo_done
lbne geo_branch_15
lda #$00
sta g_cmp
lda g_c+1
cmpa g_cmp
lblo geo_done
geo_branch_15
lda #$01
eora #$80
sta g_cmp
lda g_c
eora #$80
cmpa g_cmp
lblo geo_branch_16
lbne geo_done
lda #$ff
sta g_cmp
lda g_c+1
cmpa g_cmp
lblo geo_branch_16
lbne geo_done
geo_branch_16
lda #$fe
eora #$80
sta g_cmp
lda g_d
eora #$80
cmpa g_cmp
lblo geo_done
lbne geo_branch_17
lda #$00
sta g_cmp
lda g_d+1
cmpa g_cmp
lblo geo_done
geo_branch_17
lda #$01
eora #$80
sta g_cmp
lda g_d
eora #$80
cmpa g_cmp
lblo geo_branch_18
lbne geo_done
lda #$ff
sta g_cmp
lda g_d+1
cmpa g_cmp
lblo geo_branch_18
lbne geo_done
geo_branch_18
lda #$01
sta g_status
jmp geo_line_start
geo_curve_validate
lda #$00
sta g_cmp
lda g_flags
cmpa g_cmp
lbne geo_done
geo_branch_19
lda #$00
eora #$80
sta g_cmp
lda g_c
eora #$80
cmpa g_cmp
lblo geo_done
lbne geo_branch_20
lda #$00
sta g_cmp
lda g_c+1
cmpa g_cmp
lblo geo_done
geo_branch_20
lda #$00
eora #$80
sta g_cmp
lda g_c
eora #$80
cmpa g_cmp
lblo geo_branch_21
lbne geo_done
lda #$ff
sta g_cmp
lda g_c+1
cmpa g_cmp
lblo geo_branch_21
lbne geo_done
geo_branch_21
ldd g_c
std g_rx
lda #$01
sta g_cmp
lda g_mode
cmpa g_cmp
lbne geo_branch_22
jmp geo_equal_axes
geo_branch_22
lda #$03
sta g_cmp
lda g_mode
cmpa g_cmp
lbne geo_branch_23
jmp geo_equal_axes
geo_branch_23
lda #$00
eora #$80
sta g_cmp
lda g_d
eora #$80
cmpa g_cmp
lblo geo_done
lbne geo_branch_24
lda #$00
sta g_cmp
lda g_d+1
cmpa g_cmp
lblo geo_done
geo_branch_24
lda #$00
eora #$80
sta g_cmp
lda g_d
eora #$80
cmpa g_cmp
lblo geo_branch_25
lbne geo_done
lda #$ff
sta g_cmp
lda g_d+1
cmpa g_cmp
lblo geo_branch_25
lbne geo_done
geo_branch_25
ldd g_d
std g_ry
jmp geo_axes_ready
geo_equal_axes
ldd g_c
std g_ry
geo_axes_ready
lda #$01
sta g_status
lda #$00
sta g_fill
lda #$03
sta g_cmp
lda g_mode
cmpa g_cmp
lblo geo_curve_start
geo_branch_26
lda #$01
sta g_fill
jmp geo_curve_start
geo_done
rts
geo_line_start
; Canonical ordering gives the same tie pixels when endpoints are reversed.
ldd g_a
std g_x
ldd g_b
std g_y
ldd g_c
std g_end_x
ldd g_d
std g_end_y
lda #$00
sta g_swap
lda g_end_x
eora #$80
sta g_cmp
lda g_x
eora #$80
cmpa g_cmp
lblo geo_branch_27
lbne geo_swap_endpoints
lda g_end_x+1
sta g_cmp
lda g_x+1
cmpa g_cmp
lblo geo_branch_27
lbne geo_swap_endpoints
geo_branch_27
lda g_end_x
eora #$80
sta g_cmp
lda g_x
eora #$80
cmpa g_cmp
lbne geo_line_ordered
lda g_end_x+1
sta g_cmp
lda g_x+1
cmpa g_cmp
lbne geo_line_ordered
geo_branch_28
lda g_end_y
eora #$80
sta g_cmp
lda g_y
eora #$80
cmpa g_cmp
lblo geo_line_ordered
lbne geo_branch_29
lda g_end_y+1
sta g_cmp
lda g_y+1
cmpa g_cmp
lblo geo_line_ordered
lbeq geo_line_ordered
geo_branch_29
geo_swap_endpoints
ldd g_x
std g_temp
ldd g_end_x
std g_x
ldd g_temp
std g_end_x
ldd g_y
std g_temp
ldd g_end_y
std g_y
ldd g_temp
std g_end_y
lda #$01
sta g_swap
geo_line_ordered
lda g_end_y
eora #$80
sta g_cmp
lda g_y
eora #$80
cmpa g_cmp
lbne geo_branch_30
lda g_end_y+1
sta g_cmp
lda g_y+1
cmpa g_cmp
lbne geo_branch_30
jmp geo_horizontal
geo_branch_30
lda g_end_x
eora #$80
sta g_cmp
lda g_x
eora #$80
cmpa g_cmp
lbne geo_branch_31
lda g_end_x+1
sta g_cmp
lda g_x+1
cmpa g_cmp
lbne geo_branch_31
jmp geo_vertical_line
geo_branch_31
ldd g_end_x
std g_dx
ldd g_dx
subd g_x
std g_dx
ldd g_end_y
std g_dy
ldd g_dy
subd g_y
std g_dy
ldd #$0001
std g_sy
lda #$00
eora #$80
sta g_cmp
lda g_dy
eora #$80
cmpa g_cmp
lblo geo_branch_33
lbne geo_branch_32
lda #$00
sta g_cmp
lda g_dy+1
cmpa g_cmp
lblo geo_branch_33
jmp geo_branch_32
geo_branch_33
ldd #$ffff
std g_sy
lda g_dy+1
eora #$ff
sta g_dy+1
lda g_dy
eora #$ff
sta g_dy
ldd g_dy
addd #$0001
std g_dy
geo_branch_32
lda g_dy+1
eora #$ff
sta g_dy+1
lda g_dy
eora #$ff
sta g_dy
ldd g_dy
addd #$0001
std g_dy
ldd g_dx
std g_err
ldd g_err
addd g_dy
std g_err
lda #$01
sta g_first
geo_line_loop
lda #$00
sta g_cmp
lda g_flags
cmpa g_cmp
lbne geo_branch_36
jmp geo_branch_34
geo_branch_36
lda #$00
sta g_cmp
lda g_swap
cmpa g_cmp
lbne geo_branch_38
jmp geo_branch_37
geo_branch_38
lda #$00
sta g_cmp
lda g_first
cmpa g_cmp
lbne geo_branch_35
geo_branch_39
jmp geo_branch_34
geo_branch_37
lda g_end_x
eora #$80
sta g_cmp
lda g_x
eora #$80
cmpa g_cmp
lbne geo_branch_34
lda g_end_x+1
sta g_cmp
lda g_x+1
cmpa g_cmp
lbne geo_branch_34
geo_branch_40
lda g_end_y
eora #$80
sta g_cmp
lda g_y
eora #$80
cmpa g_cmp
lbne geo_branch_41
lda g_end_y+1
sta g_cmp
lda g_y+1
cmpa g_cmp
lbne geo_branch_41
jmp geo_done
geo_branch_41
geo_branch_34
ldd g_x
std g_px
ldd g_y
std g_py
jsr geo_point
geo_branch_35
lda #$00
sta g_first
lda g_end_x
eora #$80
sta g_cmp
lda g_x
eora #$80
cmpa g_cmp
lbne geo_branch_42
lda g_end_x+1
sta g_cmp
lda g_x+1
cmpa g_cmp
lbne geo_branch_42
geo_branch_43
lda g_end_y
eora #$80
sta g_cmp
lda g_y
eora #$80
cmpa g_cmp
lbne geo_branch_44
lda g_end_y+1
sta g_cmp
lda g_y+1
cmpa g_cmp
lbne geo_branch_44
jmp geo_done
geo_branch_44
geo_branch_42
ldd g_err
std g_e2
lsl g_e2+1
rol g_e2
lda g_dy
eora #$80
sta g_cmp
lda g_e2
eora #$80
cmpa g_cmp
lblo geo_branch_45
lbne geo_branch_46
lda g_dy+1
sta g_cmp
lda g_e2+1
cmpa g_cmp
lblo geo_branch_45
geo_branch_46
ldd g_err
addd g_dy
std g_err
ldd g_x
addd #$0001
std g_x
geo_branch_45
lda g_dx
eora #$80
sta g_cmp
lda g_e2
eora #$80
cmpa g_cmp
lblo geo_branch_48
lbne geo_branch_47
lda g_dx+1
sta g_cmp
lda g_e2+1
cmpa g_cmp
lblo geo_branch_48
lbne geo_branch_47
geo_branch_48
ldd g_err
addd g_dx
std g_err
ldd g_y
addd g_sy
std g_y
geo_branch_47
jmp geo_line_loop
geo_horizontal
lda #$00
sta g_cmp
lda g_flags
cmpa g_cmp
lbne geo_branch_50
jmp geo_branch_49
geo_branch_50
lda #$00
sta g_cmp
lda g_swap
cmpa g_cmp
lbne geo_branch_52
jmp geo_branch_51
geo_branch_52
ldd g_x
addd #$0001
std g_x
jmp geo_branch_49
geo_branch_51
ldd g_end_x
addd #$ffff
std g_end_x
geo_branch_49
lda g_end_x
eora #$80
sta g_cmp
lda g_x
eora #$80
cmpa g_cmp
lblo geo_branch_53
lbne geo_done
lda g_end_x+1
sta g_cmp
lda g_x+1
cmpa g_cmp
lblo geo_branch_53
lbne geo_done
geo_branch_53
ldd g_x
std g_px
ldd g_end_x
std g_right
ldd g_y
std g_py
jsr geo_span
jmp geo_done
geo_vertical_line
lda #$00
sta g_cmp
lda g_flags
cmpa g_cmp
lbne geo_branch_55
jmp geo_branch_54
geo_branch_55
lda #$00
sta g_cmp
lda g_swap
cmpa g_cmp
lbne geo_branch_57
jmp geo_branch_56
geo_branch_57
ldd g_y
addd #$0001
std g_y
jmp geo_branch_54
geo_branch_56
ldd g_end_y
addd #$ffff
std g_end_y
geo_branch_54
lda g_end_y
eora #$80
sta g_cmp
lda g_y
eora #$80
cmpa g_cmp
lblo geo_branch_58
lbne geo_done
lda g_end_y+1
sta g_cmp
lda g_y+1
cmpa g_cmp
lblo geo_branch_58
lbne geo_done
geo_branch_58
ldd g_x
std g_px
ldd g_y
std g_py
ldd g_end_y
std g_bottom
jsr geo_vspan
jmp geo_done
geo_curve_start
; Collapsed axes are an inclusive point or straight span, never a division by zero.
lda #$00
eora #$80
sta g_cmp
lda g_rx
eora #$80
cmpa g_cmp
lbne geo_branch_59
lda #$00
sta g_cmp
lda g_rx+1
cmpa g_cmp
lbne geo_branch_59
jmp geo_curve_vertical
geo_branch_59
lda #$00
eora #$80
sta g_cmp
lda g_ry
eora #$80
cmpa g_cmp
lbne geo_branch_60
lda #$00
sta g_cmp
lda g_ry+1
cmpa g_cmp
lbne geo_branch_60
jmp geo_curve_horizontal
geo_branch_60
ldd g_rx
std g_x
lda g_x+1
eora #$ff
sta g_x+1
lda g_x
eora #$ff
sta g_x
ldd g_x
addd #$0001
std g_x
ldd #$0000
std g_y
ldd #$ffff
std g_last_y
; Squared radii and signed error increments use 32-bit storage. Radii <=255.
lda #$00
sta g_a2+3
lda #$00
sta g_a2+2
lda #$00
sta g_a2+1
lda #$00
sta g_a2
lda #$00
sta g_work+3
lda #$00
sta g_work+2
lda #$00
sta g_work+1
lda #$00
sta g_work
lda g_rx+1
sta g_work+3
lda g_rx
sta g_work+2
lda g_rx+1
sta g_mul
geo_branch_61
lda #$00
sta g_cmp
lda g_mul
cmpa g_cmp
lbne geo_branch_63
jmp geo_branch_62
geo_branch_63
lda g_mul
anda #1
lbeq geo_branch_64
lda g_a2+3
adda g_work+3
sta g_a2+3
lda g_a2+2
adca g_work+2
sta g_a2+2
lda g_a2+1
adca g_work+1
sta g_a2+1
lda g_a2
adca g_work
sta g_a2
geo_branch_64
lsr g_mul
lsl g_work+3
rol g_work+2
rol g_work+1
rol g_work
jmp geo_branch_61
geo_branch_62
lda #$00
sta g_b2+3
lda #$00
sta g_b2+2
lda #$00
sta g_b2+1
lda #$00
sta g_b2
lda #$00
sta g_work+3
lda #$00
sta g_work+2
lda #$00
sta g_work+1
lda #$00
sta g_work
lda g_ry+1
sta g_work+3
lda g_ry
sta g_work+2
lda g_ry+1
sta g_mul
geo_branch_65
lda #$00
sta g_cmp
lda g_mul
cmpa g_cmp
lbne geo_branch_67
jmp geo_branch_66
geo_branch_67
lda g_mul
anda #1
lbeq geo_branch_68
lda g_b2+3
adda g_work+3
sta g_b2+3
lda g_b2+2
adca g_work+2
sta g_b2+2
lda g_b2+1
adca g_work+1
sta g_b2+1
lda g_b2
adca g_work
sta g_b2
geo_branch_68
lsr g_mul
lsl g_work+3
rol g_work+2
rol g_work+1
rol g_work
jmp geo_branch_65
geo_branch_66
lda g_b2+3
sta g_step_x+3
lda g_b2+2
sta g_step_x+2
lda g_b2+1
sta g_step_x+1
lda g_b2
sta g_step_x
lsl g_step_x+3
rol g_step_x+2
rol g_step_x+1
rol g_step_x
lda g_a2+3
sta g_step_y+3
lda g_a2+2
sta g_step_y+2
lda g_a2+1
sta g_step_y+1
lda g_a2
sta g_step_y
lsl g_step_y+3
rol g_step_y+2
rol g_step_y+1
rol g_step_y
lda g_b2+3
sta g_curve_dx+3
lda g_b2+2
sta g_curve_dx+2
lda g_b2+1
sta g_curve_dx+1
lda g_b2
sta g_curve_dx
ldd g_rx
std g_temp
geo_branch_69
lda g_curve_dx+3
suba g_step_x+3
sta g_curve_dx+3
lda g_curve_dx+2
sbca g_step_x+2
sta g_curve_dx+2
lda g_curve_dx+1
sbca g_step_x+1
sta g_curve_dx+1
lda g_curve_dx
sbca g_step_x
sta g_curve_dx
ldd g_temp
addd #$ffff
std g_temp
lda #$00
eora #$80
sta g_cmp
lda g_temp
eora #$80
cmpa g_cmp
lbne geo_branch_69
lda #$00
sta g_cmp
lda g_temp+1
cmpa g_cmp
lbne geo_branch_69
geo_branch_70
lda g_a2+3
sta g_curve_dy+3
lda g_a2+2
sta g_curve_dy+2
lda g_a2+1
sta g_curve_dy+1
lda g_a2
sta g_curve_dy
lda g_curve_dx+3
sta g_curve_err+3
lda g_curve_dx+2
sta g_curve_err+2
lda g_curve_dx+1
sta g_curve_err+1
lda g_curve_dx
sta g_curve_err
lda g_curve_err+3
adda g_curve_dy+3
sta g_curve_err+3
lda g_curve_err+2
adca g_curve_dy+2
sta g_curve_err+2
lda g_curve_err+1
adca g_curve_dy+1
sta g_curve_err+1
lda g_curve_err
adca g_curve_dy
sta g_curve_err
geo_curve_loop
jsr geo_emit_curve
lda g_curve_err+3
sta g_curve_e2+3
lda g_curve_err+2
sta g_curve_e2+2
lda g_curve_err+1
sta g_curve_e2+1
lda g_curve_err
sta g_curve_e2
lsl g_curve_e2+3
rol g_curve_e2+2
rol g_curve_e2+1
rol g_curve_e2
lda g_curve_dx
eora #$80
sta g_cmp
lda g_curve_e2
eora #$80
cmpa g_cmp
lblo geo_branch_71
lbne geo_branch_72
lda g_curve_dx+1
sta g_cmp
lda g_curve_e2+1
cmpa g_cmp
lblo geo_branch_71
lbne geo_branch_72
lda g_curve_dx+2
sta g_cmp
lda g_curve_e2+2
cmpa g_cmp
lblo geo_branch_71
lbne geo_branch_72
lda g_curve_dx+3
sta g_cmp
lda g_curve_e2+3
cmpa g_cmp
lblo geo_branch_71
geo_branch_72
ldd g_x
addd #$0001
std g_x
lda g_curve_dx+3
adda g_step_x+3
sta g_curve_dx+3
lda g_curve_dx+2
adca g_step_x+2
sta g_curve_dx+2
lda g_curve_dx+1
adca g_step_x+1
sta g_curve_dx+1
lda g_curve_dx
adca g_step_x
sta g_curve_dx
lda g_curve_err+3
adda g_curve_dx+3
sta g_curve_err+3
lda g_curve_err+2
adca g_curve_dx+2
sta g_curve_err+2
lda g_curve_err+1
adca g_curve_dx+1
sta g_curve_err+1
lda g_curve_err
adca g_curve_dx
sta g_curve_err
geo_branch_71
lda g_curve_dy
eora #$80
sta g_cmp
lda g_curve_e2
eora #$80
cmpa g_cmp
lblo geo_branch_74
lbne geo_branch_73
lda g_curve_dy+1
sta g_cmp
lda g_curve_e2+1
cmpa g_cmp
lblo geo_branch_74
lbne geo_branch_73
lda g_curve_dy+2
sta g_cmp
lda g_curve_e2+2
cmpa g_cmp
lblo geo_branch_74
lbne geo_branch_73
lda g_curve_dy+3
sta g_cmp
lda g_curve_e2+3
cmpa g_cmp
lblo geo_branch_74
lbne geo_branch_73
geo_branch_74
ldd g_y
addd #$0001
std g_y
lda g_curve_dy+3
adda g_step_y+3
sta g_curve_dy+3
lda g_curve_dy+2
adca g_step_y+2
sta g_curve_dy+2
lda g_curve_dy+1
adca g_step_y+1
sta g_curve_dy+1
lda g_curve_dy
adca g_step_y
sta g_curve_dy
lda g_curve_err+3
adda g_curve_dy+3
sta g_curve_err+3
lda g_curve_err+2
adca g_curve_dy+2
sta g_curve_err+2
lda g_curve_err+1
adca g_curve_dy+1
sta g_curve_err+1
lda g_curve_err
adca g_curve_dy
sta g_curve_err
geo_branch_73
lda #$00
eora #$80
sta g_cmp
lda g_x
eora #$80
cmpa g_cmp
lblo geo_curve_loop
lbne geo_branch_75
lda #$00
sta g_cmp
lda g_x+1
cmpa g_cmp
lblo geo_curve_loop
lbeq geo_curve_loop
geo_branch_75
ldd #$0000
std g_x
geo_curve_tip
lda g_ry
eora #$80
sta g_cmp
lda g_y
eora #$80
cmpa g_cmp
lblo geo_branch_76
lbne geo_done
lda g_ry+1
sta g_cmp
lda g_y+1
cmpa g_cmp
lblo geo_branch_76
jmp geo_done
geo_branch_76
ldd g_y
addd #$0001
std g_y
jsr geo_emit_curve
jmp geo_curve_tip
geo_curve_vertical
ldd g_a
std g_px
ldd g_b
std g_py
ldd g_py
subd g_ry
std g_py
ldd g_b
std g_bottom
ldd g_bottom
addd g_ry
std g_bottom
jsr geo_vspan
jmp geo_done
geo_curve_horizontal
ldd g_b
std g_py
ldd g_a
std g_px
ldd g_px
subd g_rx
std g_px
ldd g_a
std g_right
ldd g_right
addd g_rx
std g_right
jsr geo_span
jmp geo_done
geo_emit_curve
lda #$00
sta g_cmp
lda g_fill
cmpa g_cmp
lbne geo_emit_fill
geo_branch_77
; Axis tests remove duplicate symmetric pixels, including XOR at the centre.
ldd g_a
std g_px
ldd g_px
subd g_x
std g_px
ldd g_b
std g_py
ldd g_py
addd g_y
std g_py
jsr geo_point
lda #$00
eora #$80
sta g_cmp
lda g_x
eora #$80
cmpa g_cmp
lbne geo_branch_79
lda #$00
sta g_cmp
lda g_x+1
cmpa g_cmp
lbne geo_branch_79
jmp geo_branch_78
geo_branch_79
ldd g_a
std g_px
ldd g_px
addd g_x
std g_px
ldd g_b
std g_py
ldd g_py
addd g_y
std g_py
jsr geo_point
geo_branch_78
lda #$00
eora #$80
sta g_cmp
lda g_y
eora #$80
cmpa g_cmp
lbne geo_branch_80
lda #$00
sta g_cmp
lda g_y+1
cmpa g_cmp
lbne geo_branch_80
jmp geo_emit_return
geo_branch_80
ldd g_a
std g_px
ldd g_px
subd g_x
std g_px
ldd g_b
std g_py
ldd g_py
subd g_y
std g_py
jsr geo_point
lda #$00
eora #$80
sta g_cmp
lda g_x
eora #$80
cmpa g_cmp
lbne geo_branch_81
lda #$00
sta g_cmp
lda g_x+1
cmpa g_cmp
lbne geo_branch_81
jmp geo_emit_return
geo_branch_81
ldd g_a
std g_px
ldd g_px
addd g_x
std g_px
ldd g_b
std g_py
ldd g_py
subd g_y
std g_py
jsr geo_point
geo_emit_return
rts
geo_emit_fill
; Only the first, widest extent for a row emits spans. Each row is written once.
lda g_last_y
eora #$80
sta g_cmp
lda g_y
eora #$80
cmpa g_cmp
lbne geo_branch_82
lda g_last_y+1
sta g_cmp
lda g_y+1
cmpa g_cmp
lbne geo_branch_82
jmp geo_emit_return
geo_branch_82
ldd g_y
std g_last_y
ldd g_a
std g_px
ldd g_px
addd g_x
std g_px
ldd g_a
std g_right
ldd g_right
subd g_x
std g_right
ldd g_b
std g_py
ldd g_py
addd g_y
std g_py
jsr geo_span
lda #$00
eora #$80
sta g_cmp
lda g_y
eora #$80
cmpa g_cmp
lbne geo_branch_83
lda #$00
sta g_cmp
lda g_y+1
cmpa g_cmp
lbne geo_branch_83
jmp geo_emit_return
geo_branch_83
ldd g_a
std g_px
ldd g_px
addd g_x
std g_px
ldd g_a
std g_right
ldd g_right
subd g_x
std g_right
ldd g_b
std g_py
ldd g_py
subd g_y
std g_py
jsr geo_span
rts
geo_point
; Scissor the original raster, preserving its decision phase outside the window.
lda g_clip_l
eora #$80
sta g_cmp
lda g_px
eora #$80
cmpa g_cmp
lblo geo_emit_return
lbne geo_branch_84
lda g_clip_l+1
sta g_cmp
lda g_px+1
cmpa g_cmp
lblo geo_emit_return
geo_branch_84
lda g_clip_r
eora #$80
sta g_cmp
lda g_px
eora #$80
cmpa g_cmp
lblo geo_branch_85
lbne geo_emit_return
lda g_clip_r+1
sta g_cmp
lda g_px+1
cmpa g_cmp
lblo geo_branch_85
jmp geo_emit_return
geo_branch_85
lda g_clip_t
eora #$80
sta g_cmp
lda g_py
eora #$80
cmpa g_cmp
lblo geo_emit_return
lbne geo_branch_86
lda g_clip_t+1
sta g_cmp
lda g_py+1
cmpa g_cmp
lblo geo_emit_return
geo_branch_86
lda g_clip_b
eora #$80
sta g_cmp
lda g_py
eora #$80
cmpa g_cmp
lblo geo_branch_87
lbne geo_emit_return
lda g_clip_b+1
sta g_cmp
lda g_py+1
cmpa g_cmp
lblo geo_branch_87
jmp geo_emit_return
geo_branch_87
ldd g_px
std bp_x0
ldd g_py
std bp_y0
jsr geo_backend_inputs
jsr bp_pixel
jmp geo_account
geo_span
lda g_clip_t
eora #$80
sta g_cmp
lda g_py
eora #$80
cmpa g_cmp
lblo geo_emit_return
lbne geo_branch_88
lda g_clip_t+1
sta g_cmp
lda g_py+1
cmpa g_cmp
lblo geo_emit_return
geo_branch_88
lda g_clip_b
eora #$80
sta g_cmp
lda g_py
eora #$80
cmpa g_cmp
lblo geo_branch_89
lbne geo_emit_return
lda g_clip_b+1
sta g_cmp
lda g_py+1
cmpa g_cmp
lblo geo_branch_89
jmp geo_emit_return
geo_branch_89
lda g_clip_l
eora #$80
sta g_cmp
lda g_right
eora #$80
cmpa g_cmp
lblo geo_emit_return
lbne geo_branch_90
lda g_clip_l+1
sta g_cmp
lda g_right+1
cmpa g_cmp
lblo geo_emit_return
geo_branch_90
lda g_clip_r
eora #$80
sta g_cmp
lda g_px
eora #$80
cmpa g_cmp
lblo geo_branch_91
lbne geo_emit_return
lda g_clip_r+1
sta g_cmp
lda g_px+1
cmpa g_cmp
lblo geo_branch_91
jmp geo_emit_return
geo_branch_91
lda g_clip_l
eora #$80
sta g_cmp
lda g_px
eora #$80
cmpa g_cmp
lblo geo_branch_93
lbne geo_branch_92
lda g_clip_l+1
sta g_cmp
lda g_px+1
cmpa g_cmp
lblo geo_branch_93
jmp geo_branch_92
geo_branch_93
ldd g_clip_l
std g_px
geo_branch_92
lda g_clip_r
eora #$80
sta g_cmp
lda g_right
eora #$80
cmpa g_cmp
lblo geo_branch_94
lbne geo_branch_95
lda g_clip_r+1
sta g_cmp
lda g_right+1
cmpa g_cmp
lblo geo_branch_94
geo_branch_95
ldd g_clip_r
std g_right
ldd g_right
addd #$ffff
std g_right
geo_branch_94
ldd g_px
std bp_x0
ldd g_py
std bp_y0
ldd g_right
std bp_x1
ldd bp_x1
addd #$0001
std bp_x1
jsr geo_backend_inputs
jsr bp_hspan
jmp geo_account
geo_vspan
lda g_clip_l
eora #$80
sta g_cmp
lda g_px
eora #$80
cmpa g_cmp
lblo geo_emit_return
lbne geo_branch_96
lda g_clip_l+1
sta g_cmp
lda g_px+1
cmpa g_cmp
lblo geo_emit_return
geo_branch_96
lda g_clip_r
eora #$80
sta g_cmp
lda g_px
eora #$80
cmpa g_cmp
lblo geo_branch_97
lbne geo_emit_return
lda g_clip_r+1
sta g_cmp
lda g_px+1
cmpa g_cmp
lblo geo_branch_97
jmp geo_emit_return
geo_branch_97
lda g_clip_t
eora #$80
sta g_cmp
lda g_bottom
eora #$80
cmpa g_cmp
lblo geo_emit_return
lbne geo_branch_98
lda g_clip_t+1
sta g_cmp
lda g_bottom+1
cmpa g_cmp
lblo geo_emit_return
geo_branch_98
lda g_clip_b
eora #$80
sta g_cmp
lda g_py
eora #$80
cmpa g_cmp
lblo geo_branch_99
lbne geo_emit_return
lda g_clip_b+1
sta g_cmp
lda g_py+1
cmpa g_cmp
lblo geo_branch_99
jmp geo_emit_return
geo_branch_99
lda g_clip_t
eora #$80
sta g_cmp
lda g_py
eora #$80
cmpa g_cmp
lblo geo_branch_101
lbne geo_branch_100
lda g_clip_t+1
sta g_cmp
lda g_py+1
cmpa g_cmp
lblo geo_branch_101
jmp geo_branch_100
geo_branch_101
ldd g_clip_t
std g_py
geo_branch_100
lda g_clip_b
eora #$80
sta g_cmp
lda g_bottom
eora #$80
cmpa g_cmp
lblo geo_branch_102
lbne geo_branch_103
lda g_clip_b+1
sta g_cmp
lda g_bottom+1
cmpa g_cmp
lblo geo_branch_102
geo_branch_103
ldd g_clip_b
std g_bottom
ldd g_bottom
addd #$ffff
std g_bottom
geo_branch_102
ldd g_px
std bp_x0
ldd g_py
std bp_y0
ldd g_bottom
std bp_y1
ldd bp_y1
addd #$0001
std bp_y1
jsr geo_backend_inputs
jsr bp_vspan
jmp geo_account
geo_backend_inputs
lda g_op
sta bp_op
lda g_pen
sta bp_pen
rts
geo_account
lda #$00
sta g_work+3
lda #$00
sta g_work+2
lda #$00
sta g_work+1
lda #$00
sta g_work
lda bp_writes+1
sta g_work+3
lda bp_writes
sta g_work+2
lda g_writes+3
adda g_work+3
sta g_writes+3
lda g_writes+2
adca g_work+2
sta g_writes+2
lda g_writes+1
adca g_work+1
sta g_writes+1
lda g_writes
adca g_work
sta g_writes
ldd g_calls
addd #$0001
std g_calls
rts
geometry_endWhat was verified
215 calls completed on this exact configuration using Asm198x 0.0.71 and Emu198x 0.39.0. Every call compares complete bitmap memory, neighbouring guards, public inputs, acceptance, byte writes and backend calls with an independent model. Cases cover all octants, reversal/ties, endpoint ownership, axes, zero radii, clipping, XOR, range extremes and rejected requests. Selected whole native frames match independently composed pixels. A wrong ellipse recurrence completed accepted draws and failed both memory and picture checks.
The radius bound also has a separate exhaustive arithmetic check: all 65,025 nonzero radius pairs fit the chosen 32-bit error path. That host check does not claim native execution of every pair. Real-hardware timing, stock-OS loading and tear-free live drawing remain separate.