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se3

Provides SE(3) rigid transformations, quaternion operations, and 3D/4D vector arithmetic as DuckDB scalar functions.

Maintainer(s): jokasimr

Compatibility Matrix

This table covers all DuckDB releases that have not reached end-of-life, including LTS releases, and shows the 2 most recent patch releases of each. Older patch releases are not listed, but the extension may be available for them as well.

Platform	1.4.4	1.4.5	1.5.5	1.5.6	2.0.0
Linux AMD64
Linux ARM64
macOS AMD64
macOS ARM64
Windows AMD64
Windows ARM64
WebAssembly

Installing and Loading

INSTALL se3 FROM community;
LOAD se3;

Example

SELECT se3_apply(
    se3_from_axis_angle(
        struct_pack(x:=1.0, y:=0.0, z:=0.0), -- translation
        struct_pack(x:=0.0, y:=0.0, z:=1.0), -- rotation axis (Z)
        pi()/2.0                             -- 90 degrees
    ),
    struct_pack(x:=1.0, y:=0.0, z:=0.0)      -- point
);                                           -- {x: 0.0, y: 2.0, z: 0.0}

About se3

This extension provides SE(3) rigid transformations, quaternion operations, and 3D/4D vector arithmetic, implemented as DuckDB scalar functions.

Features:

Sequences of rotations and translations can be combined into a single rigid transformation with 6 degrees of freedom, stored as a 7-scalar struct: 3 translation components and a 4-component unit quaternion.
Transformations translate then rotate. se3_compose(W2, W1) applies W1 first, then W2.
Transformations can be efficiently applied to points in 3D without calling trigonometric functions. See se3_apply().
Quaternion construction from axis-angle, multiplication, conjugation, and squared norms.
3D/4D vector arithmetic, norms, normalization, dot products, angles and their trigonometric ratios, projection, and rejection; 3D cross products.

For types, functions, and composition semantics, see the API reference.

Added Functions

function_name	function_type	description	comment	examples
qconj	scalar	Returns the quaternion conjugate of q.	NULL	[qconj(vvec(1.0, 2.0, 3.0, 4.0))]
qmul	scalar	Multiplies quaternions qA and qB.	NULL	[qmul(quat_from_axis_angle(vvec(0.0, 0.0, 1.0), pi()/2.0), quat_from_axis_angle(vvec(0.0, 1.0, 0.0), pi()/2.0))]
qnorm2	scalar	Returns the squared norm of quaternion q.	NULL	[qnorm2(quat_from_axis_angle(vvec(0.0, 0.0, 1.0), pi()/2.0))]
quat_from_axis_angle	scalar	Constructs a unit quaternion from axis and angle in radians. Returns NULL for a zero-length axis.	NULL	[quat_from_axis_angle(vvec(0.0, 0.0, 1.0), pi()/2.0)]
se3_apply	scalar	Applies transformation W to point p. W can be a full transformation struct, a vec3 representing only the translation part, or a quat representing only the rotation part.	NULL	[se3_apply(se3_identity(), vvec(1.0, 2.0, 3.0))]
se3_compose	scalar	Composes two transformations, applying W1 first and then W2. W1 and W2 can each be a full transformation struct, a vec3 representing only the translation part, or a quat representing only the rotation part.	NULL	[se3_compose(se3_identity(), se3_identity())]
se3_from_axis_angle	scalar	Constructs a transform from translation t and an axis-angle rotation. Returns NULL for a zero-length axis.	NULL	[se3_from_axis_angle(vvec(1.0, 0.0, 0.0), vvec(0.0, 0.0, 1.0), pi()/2.0)]
se3_identity	scalar	Returns the identity transform.	NULL	[se3_identity()]
se3_inv	scalar	Returns the inverse transformation of W. W can be a full transformation struct, a vec3 representing only the translation part, or a quat representing only the rotation part.	NULL	[se3_inv(se3_identity())]
se3_make	scalar	Constructs a transform from translation t and quaternion q.	NULL	[se3_make(vvec(1.0, 2.0, 3.0), quat_from_axis_angle(vvec(0.0, 0.0, 1.0), pi()/2.0))]
vadd	scalar	Returns the element-wise sum of a and b.	NULL	[vadd(vvec(1.0, 2.0, 3.0), vvec(4.0, 5.0, 6.0))]
vangle	scalar	Returns the angle in radians between a and b.	NULL	[vangle(vvec(1.0, 0.0, 0.0), vvec(0.0, 1.0, 0.0))]
vcos_angle	scalar	Returns vdot(a, b) / (vnorm(a) * vnorm(b)) without clamping.	NULL	[vcos_angle(vvec(1.0, 0.0, 0.0), vvec(0.0, 1.0, 0.0))]
vcot_angle	scalar	Returns the cotangent of the angle between a and b.	NULL	[vcot_angle(vvec(1.0, 0.0, 0.0), vvec(1.0, 1.0, 0.0))]
vcross	scalar	Returns the 3D cross product of a and b.	NULL	[vcross(vvec(1.0, 0.0, 0.0), vvec(0.0, 1.0, 0.0))]
vdot	scalar	Returns the dot product of a and b.	NULL	[vdot(vvec(1.0, 2.0, 3.0), vvec(4.0, 5.0, 6.0))]
vnorm	scalar	Returns the Euclidean norm of v.	NULL	[vnorm(vvec(1.0, 2.0, 3.0))]
vnorm2	scalar	Returns the squared Euclidean norm of v.	NULL	[vnorm2(vvec(1.0, 2.0, 3.0))]
vnormalize	scalar	Returns v divided by its Euclidean norm.	NULL	[vnormalize(vvec(1.0, 2.0, 3.0))]
vproj	scalar	Returns the projection of a onto b.	NULL	[vproj(vvec(2.0, 2.0, 0.0), vvec(1.0, 0.0, 0.0))]
vrej	scalar	Returns the rejection of a from b.	NULL	[vrej(vvec(2.0, 2.0, 0.0), vvec(1.0, 0.0, 0.0))]
vscale	scalar	Scales vector v by scalar s.	NULL	[vscale(vvec(1.0, 2.0, 3.0), 2.0)]
vsin_angle	scalar	Returns the sine of the angle between a and b.	NULL	[vsin_angle(vvec(1.0, 0.0, 0.0), vvec(0.0, 1.0, 0.0))]
vsub	scalar	Returns the element-wise difference a - b.	NULL	[vsub(vvec(4.0, 5.0, 6.0), vvec(1.0, 2.0, 3.0))]
vtan_angle	scalar	Returns the tangent of the angle between a and b.	NULL	[vtan_angle(vvec(1.0, 0.0, 0.0), vvec(1.0, 1.0, 0.0))]
vvec	scalar	Creates a vec3 from x, y, and z components.	NULL	[vvec(1.0, 2.0, 3.0)]
vvec	scalar	Creates a vec4 from w, x, y, and z components.	NULL	[vvec(1.0, 2.0, 3.0, 4.0)]

Overloaded Functions

This extension does not add any function overloads.

Added Types

This extension does not add any types.

Added Settings

name	description	input_type	scope	aliases	typed_value
temp_directory	Set the directory to which temporary files are written.	VARCHAR	GLOBAL	[]	post.db.tmp

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