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:
ld a,0
ld (POSITION),a
ld (HIT),a
ld (VALID),a
ld (OLD_POSITION),a
ld (TARGET),a
ld (SIZE),a
ld (WALL_START),a
ld (WALL_END),a
ld (T0),a
ld (T1),a
ret
swept_axis_collision_step:
; POSITION = OLD_POSITION
ld a,(OLD_POSITION)
ld (POSITION),a
; HIT = 0
ld a,0
ld (HIT),a
; VALID = 0
ld a,0
ld (VALID),a
; if SIZE == 0:
ld a,(SIZE)
cp 0
jp z,swept_axis_collision_L1
jp swept_axis_collision_L2
swept_axis_collision_L1:
; return
ret
jp swept_axis_collision_L3
swept_axis_collision_L2:
swept_axis_collision_L3:
; if WALL_START >= WALL_END:
ld a,(WALL_START)
ld b,a
ld a,(WALL_END)
ld c,a
ld a,b
cp c
jp nc,swept_axis_collision_L4
jp swept_axis_collision_L5
swept_axis_collision_L4:
; return
ret
jp swept_axis_collision_L6
swept_axis_collision_L5:
swept_axis_collision_L6:
; T0 = OLD_POSITION + SIZE
ld a,(OLD_POSITION)
ld b,a
ld a,(SIZE)
ld c,a
ld a,b
add a,c
ld (T0),a
; if T0 < OLD_POSITION:
ld a,(T0)
ld b,a
ld a,(OLD_POSITION)
ld c,a
ld a,b
cp c
jp c,swept_axis_collision_L7
jp swept_axis_collision_L8
swept_axis_collision_L7:
; return
ret
jp swept_axis_collision_L9
swept_axis_collision_L8:
swept_axis_collision_L9:
; T1 = TARGET + SIZE
ld a,(TARGET)
ld b,a
ld a,(SIZE)
ld c,a
ld a,b
add a,c
ld (T1),a
; if T1 < TARGET:
ld a,(T1)
ld b,a
ld a,(TARGET)
ld c,a
ld a,b
cp c
jp c,swept_axis_collision_L10
jp swept_axis_collision_L11
swept_axis_collision_L10:
; return
ret
jp swept_axis_collision_L12
swept_axis_collision_L11:
swept_axis_collision_L12:
; if OLD_POSITION < WALL_END:
ld a,(OLD_POSITION)
ld b,a
ld a,(WALL_END)
ld c,a
ld a,b
cp c
jp c,swept_axis_collision_L13
jp swept_axis_collision_L14
swept_axis_collision_L13:
; if T0 > WALL_START:
ld a,(T0)
ld b,a
ld a,(WALL_START)
ld c,a
ld a,b
cp c
jp z,swept_axis_collision_L17
jp nc,swept_axis_collision_L16
jp swept_axis_collision_L17
swept_axis_collision_L16:
; return
ret
jp swept_axis_collision_L18
swept_axis_collision_L17:
swept_axis_collision_L18:
jp swept_axis_collision_L15
swept_axis_collision_L14:
swept_axis_collision_L15:
; VALID = 1
ld a,1
ld (VALID),a
; POSITION = TARGET
ld a,(TARGET)
ld (POSITION),a
; if TARGET > OLD_POSITION:
ld a,(TARGET)
ld b,a
ld a,(OLD_POSITION)
ld c,a
ld a,b
cp c
jp z,swept_axis_collision_L20
jp nc,swept_axis_collision_L19
jp swept_axis_collision_L20
swept_axis_collision_L19:
; if T0 <= WALL_START:
ld a,(T0)
ld b,a
ld a,(WALL_START)
ld c,a
ld a,b
cp c
jp c,swept_axis_collision_L22
jp z,swept_axis_collision_L22
jp swept_axis_collision_L23
swept_axis_collision_L22:
; if T1 >= WALL_START:
ld a,(T1)
ld b,a
ld a,(WALL_START)
ld c,a
ld a,b
cp c
jp nc,swept_axis_collision_L25
jp swept_axis_collision_L26
swept_axis_collision_L25:
; POSITION = WALL_START - SIZE
ld a,(WALL_START)
ld b,a
ld a,(SIZE)
ld c,a
ld a,b
sub c
ld (POSITION),a
; HIT = 1
ld a,1
ld (HIT),a
jp swept_axis_collision_L27
swept_axis_collision_L26:
swept_axis_collision_L27:
jp swept_axis_collision_L24
swept_axis_collision_L23:
swept_axis_collision_L24:
jp swept_axis_collision_L21
swept_axis_collision_L20:
swept_axis_collision_L21:
; if TARGET < OLD_POSITION:
ld a,(TARGET)
ld b,a
ld a,(OLD_POSITION)
ld c,a
ld a,b
cp c
jp c,swept_axis_collision_L28
jp swept_axis_collision_L29
swept_axis_collision_L28:
; if OLD_POSITION >= WALL_END:
ld a,(OLD_POSITION)
ld b,a
ld a,(WALL_END)
ld c,a
ld a,b
cp c
jp nc,swept_axis_collision_L31
jp swept_axis_collision_L32
swept_axis_collision_L31:
; if TARGET <= WALL_END:
ld a,(TARGET)
ld b,a
ld a,(WALL_END)
ld c,a
ld a,b
cp c
jp c,swept_axis_collision_L34
jp z,swept_axis_collision_L34
jp swept_axis_collision_L35
swept_axis_collision_L34:
; POSITION = WALL_END
ld a,(WALL_END)
ld (POSITION),a
; HIT = 1
ld a,1
ld (HIT),a
jp swept_axis_collision_L36
swept_axis_collision_L35:
swept_axis_collision_L36:
jp swept_axis_collision_L33
swept_axis_collision_L32:
swept_axis_collision_L33:
jp swept_axis_collision_L30
swept_axis_collision_L29:
swept_axis_collision_L30:
ret
component_end:Machine contract
AF/BC/DE/HL may change; IX/IY are preserved. A direct CALL 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 48K diagnostic boots through ROM tape loading and USR, disables interrupts and owns the screen. The helper performs no port or screen writes.
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
org $8000
CUSTOM equ 0
BROKEN equ 0
COYOTE_STEPS equ 4
BUFFER_STEPS equ 4
TEXT_CAP equ 8
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 7
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
include "data.inc"
include "cases.inc"
include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
POSITION: defb 0
HIT: defb 0
VALID: defb 0
OLD_POSITION: defb 0
TARGET: defb 0
SIZE: defb 0
WALL_START: defb 0
WALL_END: defb 0
T0: defb 0
T1: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
end startA client retaining state between calls
preview_rules:
if CUSTOM
; OLD_POSITION = 20
ld a,20
ld (OLD_POSITION),a
; TARGET = 2
ld a,2
ld (TARGET),a
; SIZE = 2
ld a,2
ld (SIZE),a
; WALL_START = 10
ld a,10
ld (WALL_START),a
; WALL_END = 12
ld a,12
ld (WALL_END),a
if BROKEN
; TARGET = OLD_POSITION
ld a,(OLD_POSITION)
ld (TARGET),a
endif
call checked_step
call emit_state
ret
else
; OLD_POSITION = 2
ld a,2
ld (OLD_POSITION),a
; TARGET = 20
ld a,20
ld (TARGET),a
; SIZE = 3
ld a,3
ld (SIZE),a
; WALL_START = 10
ld a,10
ld (WALL_START),a
; WALL_END = 12
ld a,12
ld (WALL_END),a
if BROKEN
; TARGET = OLD_POSITION
ld a,(OLD_POSITION)
ld (TARGET),a
endif
call checked_step
call emit_state
endif
retCustomise 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
org $8000
CUSTOM equ 1
BROKEN equ 0
COYOTE_STEPS equ 2
BUFFER_STEPS equ 2
TEXT_CAP equ 4
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 49
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
include "data.inc"
include "cases.inc"
include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
POSITION: defb 0
HIT: defb 0
VALID: defb 0
OLD_POSITION: defb 0
TARGET: defb 0
SIZE: defb 0
WALL_START: defb 0
WALL_END: defb 0
T0: defb 0
T1: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
end startThe 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
org $8000
CUSTOM equ 0
BROKEN equ 1
COYOTE_STEPS equ 4
BUFFER_STEPS equ 4
TEXT_CAP equ 8
PROPERTY_COUNT equ 16
STREAM_BYTES equ 13
CRC_POLY equ 7
include "caller.inc"
include "exercise.inc"
component_start:
include "component.inc"
include "data.inc"
include "cases.inc"
include "../../physics/rectangle-overlap/display.inc"
code_end:
STATE:
POSITION: defb 0
HIT: defb 0
VALID: defb 0
OLD_POSITION: defb 0
TARGET: defb 0
SIZE: defb 0
WALL_START: defb 0
WALL_END: defb 0
T0: defb 0
T1: defb 0
input_ptr: defw 0
output_ptr: defw 0
cases_left: defb 0
ready: defb 0
preview: defs 8,0
OUTPUT: defs 1300,0
end start
Cost and alternatives
The measured helper extent is 356 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 48K PAL ROM tape load and USR, 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.