Reflect a Surface-normal Speed with Restitution on Spectrum

A bounce can lose speed along a wall’s normal while keeping its sideways motion.

Use it in a project

NORMAL_IN is an unsigned incoming speed magnitude. DIRECTION_IN is 0 or 1 for its sign along the chosen axis. RESTITUTION is 0–4 quarters. Return NORMAL_OUT=floor(NORMAL_IN*RESTITUTION/4), reverse the direction, and copy the encoded tangent byte unchanged. Invalid direction/restitution returns zero outputs and VALID=0. The caller supplies a surface-aligned basis and establishes a genuine incoming contact.

Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: NORMAL_OUT, DIRECTION_OUT, TANGENT_OUT, VALID, NORMAL_IN, DIRECTION_IN, TANGENT_IN, RESTITUTION. They occupy 8 contiguous bytes. Also reserve the private workspace: T0, T1, T2, T3 (4 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.

Call surface_response_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 surface_response_step whenever the described event occurs. The helper reads no device, waits for no frame and installs no interrupt handler.

Split speed into quotient and remainder on division by four. Multiply those small parts by at most four before combining them, retaining the full result without overflowing a byte product.

Reusable initialisation and service

; SPDX-License-Identifier: MIT
; Reflect a Surface-normal Speed with Restitution. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
surface_response_init:
    ld a,0
    ld (NORMAL_OUT),a
    ld (DIRECTION_OUT),a
    ld (TANGENT_OUT),a
    ld (VALID),a
    ld (NORMAL_IN),a
    ld (DIRECTION_IN),a
    ld (TANGENT_IN),a
    ld (RESTITUTION),a
    ld (T0),a
    ld (T1),a
    ld (T2),a
    ld (T3),a
    ret
surface_response_step:
; NORMAL_OUT = 0
    ld a,0
    ld (NORMAL_OUT),a
; DIRECTION_OUT = 0
    ld a,0
    ld (DIRECTION_OUT),a
; TANGENT_OUT = 0
    ld a,0
    ld (TANGENT_OUT),a
; VALID = 0
    ld a,0
    ld (VALID),a
; if DIRECTION_IN > 1:
    ld a,(DIRECTION_IN)
    cp 1
    jp z,surface_response_L2
    jp nc,surface_response_L1
    jp surface_response_L2
surface_response_L1:
; return
    ret
    jp surface_response_L3
surface_response_L2:
surface_response_L3:
; if RESTITUTION > 4:
    ld a,(RESTITUTION)
    cp 4
    jp z,surface_response_L5
    jp nc,surface_response_L4
    jp surface_response_L5
surface_response_L4:
; return
    ret
    jp surface_response_L6
surface_response_L5:
surface_response_L6:
; VALID = 1
    ld a,1
    ld (VALID),a
; DIRECTION_OUT = DIRECTION_IN ^ 1
    ld a,(DIRECTION_IN)
    xor 1
    ld (DIRECTION_OUT),a
; TANGENT_OUT = TANGENT_IN
    ld a,(TANGENT_IN)
    ld (TANGENT_OUT),a
; T0 = NORMAL_IN >> 2
    ld a,(NORMAL_IN)
    srl a
    srl a
    ld (T0),a
; T1 = NORMAL_IN & 3
    ld a,(NORMAL_IN)
    and 3
    ld (T1),a
; T2 = 0
    ld a,0
    ld (T2),a
; T3 = RESTITUTION
    ld a,(RESTITUTION)
    ld (T3),a
; while T3 != 0:
surface_response_L7:
    ld a,(T3)
    cp 0
    jp nz,surface_response_L8
    jp surface_response_L9
surface_response_L8:
; NORMAL_OUT = NORMAL_OUT + T0
    ld a,(NORMAL_OUT)
    ld b,a
    ld a,(T0)
    ld c,a
    ld a,b
    add a,c
    ld (NORMAL_OUT),a
; T2 = T2 + T1
    ld a,(T2)
    ld b,a
    ld a,(T1)
    ld c,a
    ld a,b
    add a,c
    ld (T2),a
; T3 = T3 - 1
    ld a,(T3)
    sub 1
    ld (T3),a
    jp surface_response_L7
surface_response_L9:
; T2 = T2 >> 2
    ld a,(T2)
    srl a
    srl a
    ld (T2),a
; NORMAL_OUT = NORMAL_OUT + T2
    ld a,(NORMAL_OUT)
    ld b,a
    ld a,(T2)
    ld c,a
    ld a,b
    add a,c
    ld (NORMAL_OUT),a
    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:
NORMAL_OUT: defb 0
DIRECTION_OUT: defb 0
TANGENT_OUT: defb 0
VALID: defb 0
NORMAL_IN: defb 0
DIRECTION_IN: defb 0
TANGENT_IN: defb 0
RESTITUTION: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: 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

A client retaining state between calls

preview_rules:
    if CUSTOM
; NORMAL_IN = 255
    ld a,255
    ld (NORMAL_IN),a
; DIRECTION_IN = 0
    ld a,0
    ld (DIRECTION_IN),a
; TANGENT_IN = 128
    ld a,128
    ld (TANGENT_IN),a
; RESTITUTION = 4
    ld a,4
    ld (RESTITUTION),a
    if BROKEN
; RESTITUTION = 4
    ld a,4
    ld (RESTITUTION),a
    endif
    call checked_step
    call emit_state
    ret
    else
; NORMAL_IN = 11
    ld a,11
    ld (NORMAL_IN),a
; DIRECTION_IN = 1
    ld a,1
    ld (DIRECTION_IN),a
; TANGENT_IN = 254
    ld a,254
    ld (TANGENT_IN),a
; RESTITUTION = 3
    ld a,3
    ld (RESTITUTION),a
    if BROKEN
; RESTITUTION = 4
    ld a,4
    ld (RESTITUTION),a
    endif
    call checked_step
    call emit_state
    endif
    ret

Customise it

Use a perfectly elastic bounce at the largest byte speed. 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:
NORMAL_OUT: defb 0
DIRECTION_OUT: defb 0
TANGENT_OUT: defb 0
VALID: defb 0
NORMAL_IN: defb 0
DIRECTION_IN: defb 0
TANGENT_IN: defb 0
RESTITUTION: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: 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

The custom diagnostic row is FF 01 80 01 FF 00 80 04. The full client trace in the source explains how it gets there.

Mistake and repair

The wrong caller forces perfectly elastic restitution. A speed of eleven returns eleven instead of eight, so the intended energy loss disappears. Preserve the material’s chosen coefficient.

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:
NORMAL_OUT: defb 0
DIRECTION_OUT: defb 0
TANGENT_OUT: defb 0
VALID: defb 0
NORMAL_IN: defb 0
DIRECTION_IN: defb 0
TANGENT_IN: defb 0
RESTITUTION: defb 0
T0: defb 0
T1: defb 0
T2: defb 0
T3: 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 215 code bytes; public state is 8 bytes and private scratch is 4 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.

At most four accumulation stages. The 68000 can use word multiplication and a shift; the explicit byte decomposition makes the small-machine representation visible. Repeated bounces lose an extra fraction through integer rounding.

The coefficient is a speed ratio, not an energy ratio. This is an axis/surface-basis response, not arbitrary-angle collision detection, friction, penetration resolution or mass exchange. For zero normal speed, the returned direction bit is immaterial.

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

Reflected axis motion: Boundary reflection and impact restitution are different decisions: one chooses contact, the other chooses returned speed.

The Craft · Maths for Games · Source and native evidence.