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geometry(2): corrections and improvements

The dot and inner products are not the same, and neither are cross and
outer ones.
Trimmed function signatures—similar to those in draw(2)—were added to
aid in comprehension.

--- a/sys/man/2/geometry

+++ b/sys/man/2/geometry

@@ -164,7 +164,7 @@

 Name

 Description

 .TP

-.B flerp

+.B flerp(\fIa\fP,\fIb\fP,\fIt\fP)

 Performs a linear interpolation by a factor of

 .I t

 between

@@ -173,7 +173,7 @@

 .IR b ,

 and returns the result.

 .TP

-.B fclamp

+.B fclamp(\fIn\fP,\fImin\fP,\fImax\fP)

 Constrains

 .I n

 to a value between

@@ -193,13 +193,13 @@

 Name

 Description

 .TP

-.B Pt2

+.B Pt2(\fIx\fP,\fIy\fP,\fIw\fP)

 Constructor function for a Point2 point.

 .TP

-.B Vec2

+.B Vec2(\fIx\fP,\fIy\fP)

 Constructor function for a Point2 vector.

 .TP

-.B addpt2

+.B addpt2(\fIa\fP,\fIb\fP)

 Creates a new 2D point out of the sum of

 .IR a 's

 and

@@ -206,7 +206,7 @@

 .IR b 's

 components.

 .TP

-subpt2

+.B subpt2(\fIa\fP,\fIb\fP)

 Creates a new 2D point out of the substraction of

 .IR a 's

 by

@@ -213,19 +213,19 @@

 .IR b 's

 components.

 .TP

-mulpt2

+.B mulpt2(\fIp\fP,\fIs\fP)

 Creates a new 2D point from multiplying

 .IR p 's

 components by the scalar

 .IR s .

 .TP

-divpt2

+.B divpt2(\fIp\fP,\fIs\fP)

 Creates a new 2D point from dividing

 .IR p 's

 components by the scalar

 .IR s .

 .TP

-lerp2

+.B lerp2(\fIa\fP,\fIb\fP,\fIt\fP)

 Performs a linear interpolation between the 2D points

 .I a

 and

@@ -234,22 +234,22 @@

 .IR t ,

 and returns the result.

 .TP

-dotvec2

+.B dotvec2(\fIa\fP,\fIb\fP)

 Computes the dot product of vectors

 .I a

 and

 .IR b .

 .TP

-vec2len

+.B vec2len(\fIv\fP)

 Computes the length—magnitude—of vector

 .IR v .

 .TP

-normvec2

+.B normvec2(\fIv\fP)

 Normalizes the vector

 .I v

 and returns a new 2D point.

 .TP

-edgeptcmp

+.B edgeptcmp(\fIe0\fP,\fIe1\fP,\fIp\fP)

 Performs a comparison between an edge, defined by a directed line from

 .I e0

 to

@@ -260,7 +260,7 @@

 the left, the result is <0; otherwise—when the point is on the line—,

 it returns 0.

 .TP

-ptinpoly

+.B ptinpoly(\fIp\fP,\fIpts\fP,\fInpts\fP)

 Returns 1 if the 2D point

 .I p

 lies within the

@@ -269,13 +269,13 @@

 .IR pts ,

 0 otherwise.

 .TP

-Pt3

+.B Pt3(\fIx\fP,\fIy\fP,\fIz\fP,\fIw\fP)

 Constructor function for a Point3 point.

 .TP

-Vec3

+.B Vec3(\fIx\fP,\fIy\fP,\fIz\fP)

 Constructor function for a Point3 vector.

 .TP

-addpt3

+.B addpt3(\fIa\fP,\fIb\fP)

 Creates a new 3D point out of the sum of

 .IR a 's

 and

@@ -282,7 +282,7 @@

 .IR b 's

 components.

 .TP

-subpt3

+.B subpt3(\fIa\fP,\fIb\fP)

 Creates a new 3D point out of the substraction of

 .IR a 's

 by

@@ -289,19 +289,19 @@

 .IR b 's

 components.

 .TP

-mulpt3

+.B mulpt3(\fIp\fP,\fIs\fP)

 Creates a new 3D point from multiplying

 .IR p 's

 components by the scalar

 .IR s .

 .TP

-divpt3

+.B divpt3(\fIp\fP,\fIs\fP)

 Creates a new 3D point from dividing

 .IR p 's

 components by the scalar

 .IR s .

 .TP

-lerp3

+.B lerp3(\fIa\fP,\fIb\fP,\fIt\fP)

 Performs a linear interpolation between the 3D points

 .I a

 and

@@ -310,23 +310,23 @@

 .IR t ,

 and returns the result.

 .TP

-dotvec3

-Computes the dot/inner product of vectors

+.B dotvec3(\fIa\fP,\fIb\fP)

+Computes the dot product of vectors

 .I a

 and

 .IR b .

 .TP

-crossvec3

-Computes the cross/outer product of vectors

+.B crossvec3(\fIa\fP,\fIb\fP)

+Computes the cross product of vectors

 .I a

 and

 .IR b .

 .TP

-vec3len

+.B vec3len(\fIv\fP)

 Computes the length—magnitude—of vector

 .IR v .

 .TP

-normvec3

+.B normvec3(\fIv\fP)

 Normalizes the vector

 .I v

 and returns a new 3D point.

@@ -335,12 +335,12 @@

 Name

 Description

 .TP

-identity

+.B identity(\fIm\fP)

 Initializes

 .I m

 into an identity, 3x3 matrix.

 .TP

-addm

+.B addm(\fIa\fP,\fIb\fP)

 Sums the matrices

 .I a

 and

@@ -348,7 +348,7 @@

 and stores the result back in

 .IR a .

 .TP

-subm

+.B subm(\fIa\fP,\fIb\fP)

 Substracts the matrix

 .I a

 by

@@ -356,7 +356,7 @@

 and stores the result back in

 .IR a .

 .TP

-mulm

+.B mulm(\fIa\fP,\fIb\fP)

 Multiplies the matrices

 .I a

 and

@@ -364,7 +364,7 @@

 and stores the result back in

 .IR a .

 .TP

-smulm

+.B smulm(\fIm\fP,\fIs\fP)

 Multiplies every element of

 .I m

 by the scalar

@@ -371,32 +371,32 @@

 .IR s ,

 storing the result in m.

 .TP

-transposem

+.B transposem(\fIm\fP)

 Transforms the matrix

 .I m

 into its transpose.

 .TP

-detm

+.B detm(\fIm\fP)

 Computes the determinant of

 .I m

 and returns the result.

 .TP

-tracem

+.B tracem(\fIm\fP)

 Computes the trace of

 .I m

 and returns the result.

 .TP

-adjm

+.B adjm(\fIm\fP)

 Transforms the matrix

 .I m

 into its adjoint.

 .TP

-invm

+.B invm(\fIm\fP)

 Transforms the matrix

 .I m

 into its inverse.

 .TP

-xform

+.B xform(\fIp\fP,\fIm\fP)

 Transforms the point

 .I p

 by the matrix

@@ -403,12 +403,12 @@

 .I m

 and returns the new 2D point.

 .TP

-identity3

+.B identity3(\fIm\fP)

 Initializes

 .I m

 into an identity, 4x4 matrix.

 .TP

-addm3

+.B addm3(\fIa\fP,\fIb\fP)

 Sums the matrices

 .I a

 and

@@ -416,7 +416,7 @@

 and stores the result back in

 .IR a .

 .TP

-subm3

+.B subm3(\fIa\fP,\fIb\fP)

 Substracts the matrix

 .I a

 by

@@ -424,7 +424,7 @@

 and stores the result back in

 .IR a .

 .TP

-mulm3

+.B mulm3(\fIa\fP,\fIb\fP)

 Multiplies the matrices

 .I a

 and

@@ -432,7 +432,7 @@

 and stores the result back in

 .IR a .

 .TP

-smulm3

+.B smulm3(\fIm\fP,\fIs\fP)

 Multiplies every element of

 .I m

 by the scalar

@@ -439,32 +439,32 @@

 .IR s ,

 storing the result in m.

 .TP

-transposem3

+.B transposem3(\fIm\fP)

 Transforms the matrix

 .I m

 into its transpose.

 .TP

-detm3

+.B detm3(\fIm\fP)

 Computes the determinant of

 .I m

 and returns the result.

 .TP

-tracem3

+.B tracem3(\fIm\fP)

 Computes the trace of

 .I m

 and returns the result.

 .TP

-adjm3

+.B adjm3(\fIm\fP)

 Transforms the matrix

 .I m

 into its adjoint.

 .TP

-invm3

+.B invm3(\fIm\fP)

 Transforms the matrix

 .I m

 into its inverse.

 .TP

-xform3

+.B xform3(\fIp\fP,\fIm\fP)

 Transforms the point

 .I p

 by the matrix

@@ -478,15 +478,15 @@

 Name

 Description

 .TP

-Quat

+.B Quat(\fIr\fP,\fIi\fP,\fIj\fP,\fIk\fP)

 Constructor function for a Quaternion.

 .TP

-Quatvec

+.B Quatvec(\fIr\fP,\fIv\fP)

 Constructor function for a Quaternion that takes the imaginary part in

 the form of a vector

 .IR v .

 .TP

-addq

+.B addq(\fIa\fP,\fIb\fP)

 Creates a new quaternion out of the sum of

 .IR a 's

 and

@@ -493,7 +493,7 @@

 .IR b 's

 components.

 .TP

-subq

+.B subq(\fIa\fP,\fIb\fP)

 Creates a new quaternion from the substraction of

 .IR a 's

 by

@@ -500,7 +500,7 @@

 .IR b 's

 components.

 .TP

-mulq

+.B mulq(\fIa\fP,\fIb\fP)

 Multiplies

 .I a

 and

@@ -507,7 +507,7 @@

 .I b

 and returns a new quaternion.

 .TP

-smulq

+.B smulq(\fIq\fP,\fIs\fP)

 Multiplies each of the components of

 .I q

 by the scalar

@@ -514,7 +514,7 @@

 .IR s ,

 returning a new quaternion.

 .TP

-sdivq

+.B sdivq(\fIq\fP,\fIs\fP)

 Divides each of the components of

 .I q

 by the scalar

@@ -521,7 +521,7 @@

 .IR s ,

 returning a new quaternion.

 .TP

-dotq

+.B dotq(\fIq\fP,\fIr\fP)

 Computes the dot-product of

 .I q

 and

@@ -528,22 +528,22 @@

 .IR r ,

 and returns the result.

 .TP

-invq

+.B invq(\fIq\fP)

 Computes the inverse of

 .I q

 and returns a new quaternion out of it.

 .TP

-qlen

+.B qlen(\fIq\fP)

 Computes

 .IR q 's

 length—magnitude—and returns the result.

 .TP

-normq

+.B normq(\fIq\fP)

 Normalizes

 .I q

 and returns a new quaternion out of it.

 .TP

-slerp

+.B slerp(\fIq\fP,\fIr\fP,\fIt\fP)

 Performs a spherical linear interpolation between the quaternions

 .I q

 and

@@ -552,7 +552,7 @@

 .IR t ,

 and returns the result.

 .TP

-qrotate

+.B qrotate(\fIp\fP,\fIaxis\fP,\fIθ\fP)

 Returns the result of rotating the point

 .I p

 around the vector

@@ -579,7 +579,7 @@

 Name

 Description

 .TP

-rframexform

+.B rframexform(\fIp\fP,\fIrf\fP)

 Transforms the point

 .IR p ,

 relative to origin O, into the frame of reference

@@ -588,7 +588,7 @@

 .BR rf.p ,

 which is itself also relative to O. It then returns the new 2D point.

 .TP

-rframexform3

+.B rframexform3(\fIp\fP,\fIrf\fP)

 Transforms the point

 .IR p ,

 relative to origin O, into the frame of reference

@@ -597,7 +597,7 @@

 .BR rf.p ,

 which is itself also relative to O. It then returns the new 3D point.

 .TP

-invrframexform

+.B invrframexform(\fIp\fP,\fIrf\fP)

 Transforms the point

 .IR p ,

 relative to

@@ -604,7 +604,7 @@

 .BR rf.p ,

 into the frame of reference O, assumed to have an orthonormal basis.

 .TP

-invrframexform3

+.B invrframexform3(\fIp\fP,\fIrf\fP)

 Transforms the point

 .IR p ,

 relative to

@@ -615,12 +615,12 @@

 Name

 Description

 .TP

-centroid

+.B centroid(\fIt\fP)

 Returns the geometric center of

 .B Triangle2

 .IR t .

 .TP

-barycoords

+.B barycoords(\fIt\fP,\fIp\fP)

 Returns a 3D point that represents the barycentric coordinates of the

 2D point

 .I p

@@ -627,7 +627,7 @@

 relative to the triangle

 .IR t .

 .TP

-centroid3

+.B centroid3(\fIt\fP)

 Returns the geometric center of

 .B Triangle3

 .IR t .