Query a Small Slope Height Profile on NES | Pattern Library

A sloping tile needs a surface at each horizontal position, not one flat collision edge.

NES shows the working diagnostic row 06 64 00 65 01 07 06 05. — A completed native caller displays 06 64 00 65 01 07 06 05. The public field order below identifies these bytes; the capture is a state diagnostic, not a recording of a finished game.

Use it in a project

LOCAL_X 0–7 selects one of eight unsigned height offsets H0–H7. MIRROR nonzero reverses the profile. Add BASE_Y to the selected offset only if the result fits 0–255. SURFACE is 255 and VALID=0 on invalid x or overflow. The height profile remains unchanged.

Include component.inc once (MOS callers include the shared 6502 implementation through it). Reserve the public fields in this exact order: LOCAL_X, BASE_Y, MIRROR, SURFACE, VALID, H0, H1, H2, H3, H4, H5, H6, H7. They occupy 13 contiguous bytes. Also reserve the private workspace: T0, T1, T2 (3 bytes). Array names in the explanation refer to the numbered consecutive bindings, such as C0, C1 and so on.

Call slope_height_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 slope_height_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 inside the helper
Supply before service	LOCAL_X, BASE_Y, MIRROR and H0–H7
Read after service	SURFACE and VALID

A height profile is a tiny lookup table. Mirroring changes its index rather than duplicating the data. The returned surface is useful to a crossing test, but querying a slope alone cannot decide whether an actor should land.

Reusable initialisation and service

6502.inc

; SPDX-License-Identifier: MIT
; Query a Small Slope Height Profile. See README.md for the byte interface and ownership.
; init clears the public fields and private workspace; set inputs afterwards.
slope_height_init:
    lda #0
    sta LOCAL_X
    sta BASE_Y
    sta MIRROR
    sta SURFACE
    sta VALID
    sta H0
    sta H1
    sta H2
    sta H3
    sta H4
    sta H5
    sta H6
    sta H7
    sta T0
    sta T1
    sta T2
    rts
slope_height_step:
; SURFACE = 255
    lda #255
    sta SURFACE
; VALID = 0
    lda #0
    sta VALID
; if LOCAL_X >= 8:
    lda LOCAL_X
    cmp #8
    bcs slope_height_L4
slope_height_L5:
    jmp slope_height_L2
slope_height_L4:
    jmp slope_height_L1
slope_height_L1:
; return
    rts
    jmp slope_height_L3
slope_height_L2:
slope_height_L3:
; T0 = LOCAL_X
    lda LOCAL_X
    sta T0
; if MIRROR != 0:
    lda MIRROR
    cmp #0
    bne slope_height_L9
slope_height_L10:
    jmp slope_height_L7
slope_height_L9:
    jmp slope_height_L6
slope_height_L6:
; T0 = 7 - T0
    lda #7
    sec
    sbc T0
    sta T0
    jmp slope_height_L8
slope_height_L7:
slope_height_L8:
; T1 = H[T0]
    ldx T0
    lda H0,x
    sta T1
; T2 = 255 - BASE_Y
    lda #255
    sec
    sbc BASE_Y
    sta T2
; if T1 > T2:
    lda T1
    cmp T2
    beq slope_height_L15
    bcs slope_height_L14
slope_height_L15:
    jmp slope_height_L12
slope_height_L14:
    jmp slope_height_L11
slope_height_L11:
; return
    rts
    jmp slope_height_L13
slope_height_L12:
slope_height_L13:
; SURFACE = BASE_Y + T1
    lda BASE_Y
    clc
    adc T1
    sta SURFACE
; VALID = 1
    lda #1
    sta VALID
    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. Scope or rename routine and field labels and allocate a separate block for each independent instance. 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

demo.asm

.segment "HEADER"
.byte "NES",$1a,2,1,0,0,0,0,0,0,0,0,0,0
LOCAL_X=$80
BASE_Y=$81
MIRROR=$82
SURFACE=$83
VALID=$84
H0=$85
H1=$86
H2=$87
H3=$88
H4=$89
H5=$8a
H6=$8b
H7=$8c
T0=$8d
T1=$8e
T2=$8f
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 8192-272,0

A client retaining state between calls

exercise.inc, excerpt

preview_rules:
.if CUSTOM
; LOCAL_X = 1
    lda #1
    sta LOCAL_X
; BASE_Y = 100
    lda #100
    sta BASE_Y
; H0 = 7
    lda #7
    sta H0
; H1 = 6
    lda #6
    sta H1
; H2 = 5
    lda #5
    sta H2
; H3 = 4
    lda #4
    sta H3
; H4 = 3
    lda #3
    sta H4
; H5 = 2
    lda #2
    sta H5
; H6 = 1
    lda #1
    sta H6
; H7 = 0
    lda #0
    sta H7
; MIRROR = 1
    lda #1
    sta MIRROR
.if BROKEN
; LOCAL_X = 0
    lda #0
    sta LOCAL_X
.endif
    jsr checked_step
    jsr emit_state
; LOCAL_X = 6
    lda #6
    sta LOCAL_X
.if BROKEN
; LOCAL_X = 0
    lda #0
    sta LOCAL_X
.endif
    jsr checked_step
    jsr emit_state
    rts
.else
; LOCAL_X = 1
    lda #1
    sta LOCAL_X
; BASE_Y = 100
    lda #100
    sta BASE_Y
; H0 = 7
    lda #7
    sta H0
; H1 = 6
    lda #6
    sta H1
; H2 = 5
    lda #5
    sta H2
; H3 = 4
    lda #4
    sta H3
; H4 = 3
    lda #3
    sta H4
; H5 = 2
    lda #2
    sta H5
; H6 = 1
    lda #1
    sta H6
; H7 = 0
    lda #0
    sta H7
.if BROKEN
; LOCAL_X = 0
    lda #0
    sta LOCAL_X
.endif
    jsr checked_step
    jsr emit_state
; LOCAL_X = 6
    lda #6
    sta LOCAL_X
.if BROKEN
; LOCAL_X = 0
    lda #0
    sta LOCAL_X
.endif
    jsr checked_step
    jsr emit_state
.endif
    rts

Customise it

Mirror the profile without making a second height table. 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

custom.asm

.segment "HEADER"
.byte "NES",$1a,2,1,0,0,0,0,0,0,0,0,0,0
LOCAL_X=$80
BASE_Y=$81
MIRROR=$82
SURFACE=$83
VALID=$84
H0=$85
H1=$86
H2=$87
H3=$88
H4=$89
H5=$8a
H6=$8b
H7=$8c
T0=$8d
T1=$8e
T2=$8f
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 8192-272,0

The custom diagnostic row is 06 64 01 6A 01 07 06 05. The full client trace in the source explains how it gets there.

Mistake and repair

The wrong caller replaces LOCAL_X with zero. Every query samples one column of the profile, flattening the intended surface. Keep the actual tile-local coordinate and mirror the profile only through MIRROR.

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

wrong.asm

.segment "HEADER"
.byte "NES",$1a,2,1,0,0,0,0,0,0,0,0,0,0
LOCAL_X=$80
BASE_Y=$81
MIRROR=$82
SURFACE=$83
VALID=$84
H0=$85
H1=$86
H2=$87
H3=$88
H4=$89
H5=$8a
H6=$8b
H7=$8c
T0=$8d
T1=$8e
T2=$8f
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

NES shows the deliberate error row 00 64 00 6B 01 07 06 05. — The wrong client completes with 00 64 00 6B 01 07 06 05; its changed inputs and state explain the result.

Cost and alternatives

The measured helper extent is 128 code bytes; public state is 13 bytes and private scratch is 3 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 with one profile lookup. An eight-byte profile can represent irregular shapes that a single slope equation cannot, trading data for arithmetic.

This returns geometry, not a full collision response. Convert world coordinates to tile-local x, query the surface, then decide crossing and snapping using the actor’s previous/proposed foot positions. Wide characters need multiple probes; ceilings and moving slopes need their own policy.

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

One-way platform crossing: Querying a surface gives the height; a previous-to-proposed crossing test decides whether the actor should land on it.

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