A fast object can cross a wall between frames even when neither endpoint overlaps it.
Use it in a project
Move an interval [OLD_POSITION,OLD_POSITION+SIZE) towards TARGET against [WALL_START,WALL_END). SIZE must be nonzero; both proposed endpoints plus SIZE must fit in a byte, the wall must be nonempty, and the old interval must not overlap it. Return POSITION clamped to first contact and HIT=1 when motion reaches or crosses that face. Invalid requests leave POSITION=OLD_POSITION and VALID=0.
Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: POSITION, HIT, VALID, OLD_POSITION, TARGET, SIZE, WALL_START, WALL_END. They occupy 8 contiguous bytes. Also reserve the private workspace: T0, T1 (2 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.
Call swept_axis_collision_init once at the intended reset boundary. It clears inputs as well as outputs and workspace. Set your starting state and configuration afterwards, then call swept_axis_collision_step whenever the described event occurs. The helper reads no device, waits for no frame and installs no interrupt handler.
| Ownership | Fields |
|---|---|
| Retain between calls | none |
| Supply before service | OLD_POSITION, TARGET, SIZE and wall edges |
| Read after service | POSITION, HIT and VALID |
When moving right, test the path of the right edge against the wall’s left face. Moving left tests the object’s left edge against the wall’s right face. This avoids sampling intermediate pixels.
Reusable initialisation and service
; SPDX-License-Identifier: MIT
; Sweep an Interval Along One Axis. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
swept_axis_collision_init:
lda #0
sta POSITION
sta HIT
sta VALID
sta OLD_POSITION
sta TARGET
sta SIZE
sta WALL_START
sta WALL_END
sta T0
sta T1
rts
swept_axis_collision_step:
; POSITION = OLD_POSITION
lda OLD_POSITION
sta POSITION
; HIT = 0
lda #0
sta HIT
; VALID = 0
lda #0
sta VALID
; if SIZE == 0:
lda SIZE
cmp #0
beq swept_axis_collision_L4
swept_axis_collision_L5:
jmp swept_axis_collision_L2
swept_axis_collision_L4:
jmp swept_axis_collision_L1
swept_axis_collision_L1:
; return
rts
jmp swept_axis_collision_L3
swept_axis_collision_L2:
swept_axis_collision_L3:
; if WALL_START >= WALL_END:
lda WALL_START
cmp WALL_END
bcs swept_axis_collision_L9
swept_axis_collision_L10:
jmp swept_axis_collision_L7
swept_axis_collision_L9:
jmp swept_axis_collision_L6
swept_axis_collision_L6:
; return
rts
jmp swept_axis_collision_L8
swept_axis_collision_L7:
swept_axis_collision_L8:
; T0 = OLD_POSITION + SIZE
lda OLD_POSITION
clc
adc SIZE
sta T0
; if T0 < OLD_POSITION:
lda T0
cmp OLD_POSITION
bcc swept_axis_collision_L14
swept_axis_collision_L15:
jmp swept_axis_collision_L12
swept_axis_collision_L14:
jmp swept_axis_collision_L11
swept_axis_collision_L11:
; return
rts
jmp swept_axis_collision_L13
swept_axis_collision_L12:
swept_axis_collision_L13:
; T1 = TARGET + SIZE
lda TARGET
clc
adc SIZE
sta T1
; if T1 < TARGET:
lda T1
cmp TARGET
bcc swept_axis_collision_L19
swept_axis_collision_L20:
jmp swept_axis_collision_L17
swept_axis_collision_L19:
jmp swept_axis_collision_L16
swept_axis_collision_L16:
; return
rts
jmp swept_axis_collision_L18
swept_axis_collision_L17:
swept_axis_collision_L18:
; if OLD_POSITION < WALL_END:
lda OLD_POSITION
cmp WALL_END
bcc swept_axis_collision_L24
swept_axis_collision_L25:
jmp swept_axis_collision_L22
swept_axis_collision_L24:
jmp swept_axis_collision_L21
swept_axis_collision_L21:
; if T0 > WALL_START:
lda T0
cmp WALL_START
beq swept_axis_collision_L30
bcs swept_axis_collision_L29
swept_axis_collision_L30:
jmp swept_axis_collision_L27
swept_axis_collision_L29:
jmp swept_axis_collision_L26
swept_axis_collision_L26:
; return
rts
jmp swept_axis_collision_L28
swept_axis_collision_L27:
swept_axis_collision_L28:
jmp swept_axis_collision_L23
swept_axis_collision_L22:
swept_axis_collision_L23:
; VALID = 1
lda #1
sta VALID
; POSITION = TARGET
lda TARGET
sta POSITION
; if TARGET > OLD_POSITION:
lda TARGET
cmp OLD_POSITION
beq swept_axis_collision_L35
bcs swept_axis_collision_L34
swept_axis_collision_L35:
jmp swept_axis_collision_L32
swept_axis_collision_L34:
jmp swept_axis_collision_L31
swept_axis_collision_L31:
; if T0 <= WALL_START:
lda T0
cmp WALL_START
bcc swept_axis_collision_L39
beq swept_axis_collision_L39
swept_axis_collision_L40:
jmp swept_axis_collision_L37
swept_axis_collision_L39:
jmp swept_axis_collision_L36
swept_axis_collision_L36:
; if T1 >= WALL_START:
lda T1
cmp WALL_START
bcs swept_axis_collision_L44
swept_axis_collision_L45:
jmp swept_axis_collision_L42
swept_axis_collision_L44:
jmp swept_axis_collision_L41
swept_axis_collision_L41:
; POSITION = WALL_START - SIZE
lda WALL_START
sec
sbc SIZE
sta POSITION
; HIT = 1
lda #1
sta HIT
jmp swept_axis_collision_L43
swept_axis_collision_L42:
swept_axis_collision_L43:
jmp swept_axis_collision_L38
swept_axis_collision_L37:
swept_axis_collision_L38:
jmp swept_axis_collision_L33
swept_axis_collision_L32:
swept_axis_collision_L33:
; if TARGET < OLD_POSITION:
lda TARGET
cmp OLD_POSITION
bcc swept_axis_collision_L49
swept_axis_collision_L50:
jmp swept_axis_collision_L47
swept_axis_collision_L49:
jmp swept_axis_collision_L46
swept_axis_collision_L46:
; if OLD_POSITION >= WALL_END:
lda OLD_POSITION
cmp WALL_END
bcs swept_axis_collision_L54
swept_axis_collision_L55:
jmp swept_axis_collision_L52
swept_axis_collision_L54:
jmp swept_axis_collision_L51
swept_axis_collision_L51:
; if TARGET <= WALL_END:
lda TARGET
cmp WALL_END
bcc swept_axis_collision_L59
beq swept_axis_collision_L59
swept_axis_collision_L60:
jmp swept_axis_collision_L57
swept_axis_collision_L59:
jmp swept_axis_collision_L56
swept_axis_collision_L56:
; POSITION = WALL_END
lda WALL_END
sta POSITION
; HIT = 1
lda #1
sta HIT
jmp swept_axis_collision_L58
swept_axis_collision_L57:
swept_axis_collision_L58:
jmp swept_axis_collision_L53
swept_axis_collision_L52:
swept_axis_collision_L53:
jmp swept_axis_collision_L48
swept_axis_collision_L47:
swept_axis_collision_L48:
rts
component_end:Machine contract
A/X/status may change; Y is preserved. The 2A03 has no decimal arithmetic mode. A direct JSR needs two return-address stack bytes. The helper makes no nested calls and adds no other stack use. Its named scratch is private workspace, not a pointer, a ROM variable or shared zero-page space that the game may borrow concurrently. The samples use fixed symbol bindings. Scope or rename every label and binding, including the component_end measurement marker, and allocate a separate block for each independent instance. Different helpers can also use common field names, so combining them needs separate namespaces or explicitly renamed bindings. Give each block one mutation owner.
The NROM caller owns PPU setup and background display, with NMI and DMC disabled. Table and packet sizes are bounded to fit the cartridge caller and internal RAM; the helper owns no PPU registers.
Adapt the caller
demo.asm supplies the bindings and include order. exercise.inc first runs table cases, then a separate client retaining state between calls. A game can call the public step entry directly and remove the diagnostic packet and display. Do not copy the diagnostic’s hardware takeover into an existing game loop.
Build with make ASM198X=/path/to/asm198x. The Makefile produces normal, custom, deliberately wrong and repaired programs. Tools must already be installed; the sample downloads nothing.
Bindings and include order
.segment "HEADER"
.byte "NES",$1a,2,1,0,0,0,0,0,0,0,0,0,0
POSITION=$80
HIT=$81
VALID=$82
OLD_POSITION=$83
TARGET=$84
SIZE=$85
WALL_START=$86
WALL_END=$87
T0=$88
T1=$89
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$0200
preview=OUTPUT+1400
ready=OUTPUT+1408
CUSTOM=0
BROKEN=0
COYOTE_STEPS=4
BUFFER_STEPS=4
TEXT_CAP=8
PROPERTY_COUNT=16
STREAM_BYTES=13
CRC_POLY=7
.include "caller.inc"
.include "exercise.inc"
component_start:
.include "component.inc"
.include "data.inc"
.include "cases.inc"
code_end:
.segment "VECTORS"
.word nmi,reset,irq
.segment "CHARS"
.include "../../input/controller-reading/edges-font.inc"
.res 8192-272,0A client retaining state between calls
preview_rules:
.if CUSTOM
; OLD_POSITION = 20
lda #20
sta OLD_POSITION
; TARGET = 2
lda #2
sta TARGET
; SIZE = 2
lda #2
sta SIZE
; WALL_START = 10
lda #10
sta WALL_START
; WALL_END = 12
lda #12
sta WALL_END
.if BROKEN
; TARGET = OLD_POSITION
lda OLD_POSITION
sta TARGET
.endif
jsr checked_step
jsr emit_state
rts
.else
; OLD_POSITION = 2
lda #2
sta OLD_POSITION
; TARGET = 20
lda #20
sta TARGET
; SIZE = 3
lda #3
sta SIZE
; WALL_START = 10
lda #10
sta WALL_START
; WALL_END = 12
lda #12
sta WALL_END
.if BROKEN
; TARGET = OLD_POSITION
lda OLD_POSITION
sta TARGET
.endif
jsr checked_step
jsr emit_state
.endif
rtsCustomise it
Sweep leftwards towards the opposite wall face. The maintained custom caller changes its inputs or client sequence rather than hiding a different implementation behind the same label. Compare every state of the two clients, not only their final display.
Custom client selection
.segment "HEADER"
.byte "NES",$1a,2,1,0,0,0,0,0,0,0,0,0,0
POSITION=$80
HIT=$81
VALID=$82
OLD_POSITION=$83
TARGET=$84
SIZE=$85
WALL_START=$86
WALL_END=$87
T0=$88
T1=$89
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$0200
preview=OUTPUT+1400
ready=OUTPUT+1408
CUSTOM=1
BROKEN=0
COYOTE_STEPS=2
BUFFER_STEPS=2
TEXT_CAP=4
PROPERTY_COUNT=16
STREAM_BYTES=13
CRC_POLY=49
.include "caller.inc"
.include "exercise.inc"
component_start:
.include "component.inc"
.include "data.inc"
.include "cases.inc"
code_end:
.segment "VECTORS"
.word nmi,reset,irq
.segment "CHARS"
.include "../../input/controller-reading/edges-font.inc"
.res 8192-272,0The custom diagnostic row is 0C 01 01 14 02 02 0A 0C. The full client trace in the source explains how it gets there.
Mistake and repair
The wrong caller passes the old position as the target. Nothing moves, so no sweep can detect contact. Keep the requested endpoint distinct from the current position.
The BROKEN branch lives in the sequential client, not the reusable helper. wrong.asm selects it; repaired.asm restores the normal call sequence. The repaired executable matches the normal program (for Spectrum, compare loaded CODE rather than the tape filename).
Select the deliberately wrong client
.segment "HEADER"
.byte "NES",$1a,2,1,0,0,0,0,0,0,0,0,0,0
POSITION=$80
HIT=$81
VALID=$82
OLD_POSITION=$83
TARGET=$84
SIZE=$85
WALL_START=$86
WALL_END=$87
T0=$88
T1=$89
STATE=$80
input_ptr=$70
cases_left=$72
ptr=$74
saved_y=$76
OUTPUT=$0200
preview=OUTPUT+1400
ready=OUTPUT+1408
CUSTOM=0
BROKEN=1
COYOTE_STEPS=4
BUFFER_STEPS=4
TEXT_CAP=8
PROPERTY_COUNT=16
STREAM_BYTES=13
CRC_POLY=7
.include "caller.inc"
.include "exercise.inc"
component_start:
.include "component.inc"
.include "data.inc"
.include "cases.inc"
code_end:
.segment "VECTORS"
.word nmi,reset,irq
.segment "CHARS"
.include "../../input/controller-reading/edges-font.inc"
.res 8192-272,0
Cost and alternatives
The measured helper extent is 270 code bytes; public state is 8 bytes and private scratch is 2 bytes. There are no immutable helper tables. Caller data, the test cases, return-address stack, alignment and display buffers cost additional space. These are assembled sizes, not cycle measurements.
Constant work for one wall. More obstacles require a broad phase and nearest-contact selection; subdividing movement is simpler but costs more as speed increases.
This is one axis and one static obstacle, with no initial penetration. A full 2D swept solver needs the earliest contact across candidates and a policy for the remaining movement.
Execution evidence
Four variants run on NTSC NROM, background only, DMC/NMI disabled, using Asm198x 0.0.72, Emu198x 0.44.2. Each executes 64 boundary/varied/error table cases, dirty initialisation and the separate retained-state client. An independent mathematical/container model checks every public byte after every call. This is bounded example coverage, not exhaustive correctness for every possible state.
The records retain loaded immutable code, completion, register sentinels, full packets, source/tool/firmware hashes and captures. The public gate validates these retained observations and rejects altered evidence; it does not run restricted firmware. No firmware is distributed. The eight displayed bytes are the first eight public fields, zero-padded when shorter; the packet includes every field.
Where it fits
Rectangle overlap: Endpoint overlap is useful for slow movement but does not detect a crossed obstacle.