Signed Distance Field Interchange Format

Abstract

A problem which could be seen to be limiting widespread adoption of signed distance fields is the lack of a standard interchange format between applications which would produce and consume them. For example, it would be equivalent to STL/OBJ in the following workflow, but for signed distance fields rather than polygonal meshes:

Thingiverse -----------> Blender -----------> Cura ---------> 3D Printer
             (STL/OBJ)   (BLEND)  (STL/OBJ)   (3MF) (GCODE)

This document drafts such a format.

The key difference between common 3D model interchange formats such as OBJ and STL, and an interchange format for signed distance fields, is that while polygonal models can be expressed through fairly simple tables of data, signed distance fields are mathematical functions equating locations in 3D space to distances to the nearest surface (with negative values given when below said surface).

Tabular data is considerably easier to consume than logic. To maximise the appeal of implementing this interchange format, it is important to focus on keeping its instruction set and format minimal and simplistic for machine-machine communication.

Format

A little-endian binary file.

Header

Offset	Description	Example	Description
00	Signature	`53 44 46`	"SDF"
01	Version	`00`
04	No. Dimensions	`02`	2-dimensional
		`03`	3-dimensional
05	Unit Scale	`00 00 80 3F`	Meters (1.0)
		`0A D7 23 3C`	Centimetres (0.01)

Instructions

All instructions are an instruction ID followed by the arguments required by that instruction. The result of the last instruction in the file is taken as the distance to the nearest surface.

Instruction ID

ID	A	B	C	Result	Equivalent C	Undefined Behaviour
00	Float	N/A	N/A	Float	-A
01	Float	Float	N/A	Float	A + B
02	Float	Float	N/A	Float	A - B
03	Float	Float	N/A	Float	A * B
04	Float	Float	N/A	Float	A / B	Division by zero
05	Float	N/A	N/A	Float	sinf(A)
06	Float	N/A	N/A	Float	cosf(A)
07	Float	N/A	N/A	Float	tanf(A)
08	Float	N/A	N/A	Float	asinf(A)
09	Float	N/A	N/A	Float	acosf(A)
0A	Float	N/A	N/A	Float	atanf(A)
0B	Float	N/A	N/A	Float	sinhf(A)
0C	Float	N/A	N/A	Float	coshf(A)
0D	Float	N/A	N/A	Float	tanhf(A)
0E	Float	N/A	N/A	Float	asinhf(A)
0F	Float	N/A	N/A	Float	acoshf(A)
10	Float	N/A	N/A	Float	atanhf(A)
11	Float	Float	N/A	Float	powf(A, B)
12	Float	N/A	N/A	Float	expf(A)
13	Float	N/A	N/A	Float	logf(A)
14	Float	N/A	N/A	Float	exp2f(A)
15	Float	N/A	N/A	Float	log2f(A)
16	Float	N/A	N/A	Float	sqrtf(A)
17	Float	Float	N/A	Bool	A > B	A == B
18	Bool	Float	Float	Float	A ? B : C
19	Bool	Bool	Bool	Bool	A ? B : C
1A	Bool	N/A	N/A	Bool	!A
1B	Bool	Bool	N/A	Bool	A == B
1C	Bool	Bool	N/A	Bool	A != B
1D	Bool	Bool	N/A	Bool	A && B
1E	Bool	Bool	N/A	Bool	A
1F	Float	N/A	N/A	N/A	floorf(A)
20	Float	N/A	N/A	N/A	ceilf(A)

Argument

Given four dimensions and two previous instructions:

Argument	Description
00 00 00 00	X
01 00 00 00	Y
02 00 00 00	Z
03 00 00 00	W
04 00 00 00	Previous instruction A
05 00 00 00	Previous instruction B
FF FF FF FF 33 33 DB 41	24.4 (float constant)

Example

The following file produces a unit sphere at (0, 0, 0).

53 44 46                                 // "SDF"
00                                       // Version 0
03                                       // 3-dimensional
00 00 80 3F                              // Meters
03  00 00 00 00  00 00 00 00             // X * X
03  01 00 00 00  01 00 00 00             // Y * Y
03  02 00 00 00  02 00 00 00             // Z * Z
01  03 00 00 00  04 00 00 00             // X * X + Y * Y
01  06 00 00 00  05 00 00 00             // X * X + Y * Y + Z * Z
16  07 00 00 00                          // sqrtf(X * X + Y * Y + Z * Z)
02  08 00 00 00  FF FF FF FF 00 00 80 3F // sqrtf(X * X + Y * Y + Z * Z) - 1.0f

jameswilddev/Signed Distance Field Interchange Format.md