Glyph

Version 7.22.2

- Vector3

pwu:: Vector3

Utility functions for three dimensional vectors, which are represented as a list of three real values.

Summary

pwu:: Vector3	Utility functions for three dimensional vectors, which are represented as a list of three real values.
Static Actions
zero	Return the 3 dimensional zero vector
set	Return a vector with the given x, y and z components
index	Return the value of the vector at the given index
x	Return the x component of the vector
y	Return the y component of the vector
z	Return the z component of the vector
equal	Check if two vectors are equal
notEqual	Check if two vectors are not equal
add	Add two vectors together and return the result
subtract	Subtract one vector from another and return the result
negate	Return the negation of a vector
scale	Scale a vector by a single scalar value
divide	Scale a vector by inverse of a single scalar value
multiply	Return a vector that is the components of two vectors multiplied together
cross	Return the cross product of two vectors
dot	Calculate the dot product of two vectors
normalize	Return the normalization of a vector
length	Return the length of the vector
distanceToLine	Return the distance of the vector to a line
minimum	Return a vector that has the minimum components of two vectors
maximum	Return a vector that has the maximum components of two vectors
affine	Return a vector that is the affine combination of two vectors
barycentric	Return a vector that has the barycentric coordinates of the given point in the frame of the given three vectors
intersect	Return a vector that is the intersection of the two lines specified as two point and direction pairs.

Static Actions

zero

pwu::Vector3 zero

Return the 3 dimensional zero vector

Parameters

none

Returns

a vector with the given x and y

set

pwu::Vector3 set x y z

Return a vector with the given x, y and z components

Parameters

x	the x component
y	the y component
z	the z component

Returns

a vector with the given x and y

index

pwu::Vector3 index vec i

Return the value of the vector at the given index

Parameters

vec	the vector
i	the index to get; [0, 2]

Returns

the value of the vector at the given index

x

pwu::Vector3 x vec

Return the x component of the vector

Parameters

vec	the vector

Returns

the x component of the vector

y

pwu::Vector3 y vec

Return the y component of the vector

Parameters

vec	the vector

Returns

the y component of the vector

z

pwu::Vector3 z vec

Return the z component of the vector

Parameters

vec	the vector

Returns

the z component of the vector

equal

pwu::Vector3 equal ?-tolerance tol? vec1 vec2

Check if two vectors are equal

Parameters

tol	the tolerance to check equality, 0.0 is used if not given
vec1	the first vector
vec2	the second vector

Returns

true if the vectors are equal within tolerance

notEqual

pwu::Vector3 notEqual ?-tolerance tol? vec1 vec2

Check if two vectors are not equal

Parameters

tol	the tolerance to check equality, 0.0 is used if not given
vec1	the first vector
vec2	the second vector

Returns

true if the vectors are not equal within tolerance

add

pwu::Vector3 add vec1 vec2

Add two vectors together and return the result

Parameters

vec1	the first vector
vec2	the second vector

Returns

the sum of the two vectors

subtract

pwu::Vector3 subtract vec1 vec2

Subtract one vector from another and return the result

Parameters

vec1	the first vector
vec2	the second vector

Returns

the difference of the two vectors

negate

pwu::Vector3 negate vec

Return the negation of a vector

Parameters

vec	the vector

Returns

the negated vector

scale

pwu::Vector3 scale vec scalar

Scale a vector by a single scalar value

Parameters

vec	the vector
scalar	a scalar value

Returns

a vector scaled by the scalar

divide

pwu::Vector3 divide vec scalar

Scale a vector by inverse of a single scalar value

Parameters

vec	the vector
scalar	a scalar value

Returns

a vector divided by the scalar

multiply

pwu::Vector3 multiply vec1 vec2

Return a vector that is the components of two vectors multiplied together

Parameters

vec1	the first vector
vec2	the second vector

Returns

the component multiply of the two vectors

cross

pwu::Vector3 cross vec1 vec2

Return the cross product of two vectors

Parameters

vec1	the first vector
vec2	the second vector

Returns

the cross product of the two vectors

dot

pwu::Vector3 dot vec1 vec2

Calculate the dot product of two vectors

Parameters

vec1	the first vector
vec2	the second vector

Returns

the dot product of the two vectors

normalize

pwu::Vector3 normalize ?-length lenVar? vec

Return the normalization of a vector

Parameters

vec	the vector
lenVar	a variable name to set the length of the vector before being normalized

Returns

the normalized vector

length

pwu::Vector3 length vec

Return the length of the vector

Parameters

vec	the vector

Returns

the length of the vector

distanceToLine

pwu::Vector3 distanceToLine vec pt dir

Return the distance of the vector to a line

Parameters

vec	the vector
pt	the origin point of the line
dir	the direction vector of the line

Returns

the perpendicular distance of the vector to the line

minimum

pwu::Vector3 minimum vec1 vec2

Return a vector that has the minimum components of two vectors

Parameters

vec1	the first vector
vec2	the second vector

Returns

the minimum vector

maximum

pwu::Vector3 maximum vec1 vec2

Return a vector that has the maximum components of two vectors

Parameters

vec1	the first vector
vec2	the second vector

Returns

the maximum vector

affine

pwu::Vector3 affine s vec1 vec2

Return a vector that is the affine combination of two vectors

Parameters

s	the affine scalar
vec1	the first vector
vec2	the second vector

Returns

A linearly interpolated point along the directed line from vec1 to vec2. An s of 0.0 returns vec1 and and s of 1.0 returns vec2. Values of s less than 0.0 and greater than 1.0 are valid. When s is less than 0.0, the point returned would be before vec1. When s is greater than 1.0, the point returned would be after vec2.

Example

Code

# Capture extents of all database entities
lassign [pw::Database getExtents] minExt maxExt

# Compute extents centroid
set centroidPt [pwu::Vector3 affine 0.5 $minExt $maxExt]

# Enlarge extents diagonal by 10%
set minExt10 [pwu::Vector3 affine -0.1 $minExt $maxExt]
set maxExt10 [pwu::Vector3 affine 1.1 $minExt $maxExt]

puts "minExt     : [list $minExt]"
puts "maxExt     : [list $maxExt]"
puts "centroidPt : [list $centroidPt]"
puts "minExt10   : [list $minExt10]"
puts "maxExt10   : [list $maxExt10]"

Output

minExt     : {10.000170704427509 -14.405848937908303 -9.049999999999983}
maxExt     : {40.0 65.59615106209186 50.95000000000002}
centroidPt : {25.000085352213755 25.59515106209178 20.950000000000017}
minExt10   : {7.000187774870261 -22.40604893790832 -15.049999999999985}
maxExt10   : {42.99998292955725 73.59635106209188 56.950000000000024}

barycentric

pwu::Vector3 barycentric pt vec1 vec2 vec3

Return a vector that has the barycentric coordinates of the given point in the frame of the given three vectors

Parameters

pt	the point to find the barycentric coordinates of
vec1	the first vector
vec2	the second vector
vec3	the third vector

Returns

The barycentric coordinates vector.

intersect

pwu::Vector3 intersect ?-tolerance tol? anchor1 dir1 anchor2 dir2

Return a vector that is the intersection of the two lines specified as two point and direction pairs.

Parameters

tolerance	This parameter specifies the maximum distance allowed between the closest points of approach on each line. If the tolerance is exceeded, an error is raised. A value of 0.0 (the default) or less disables this check.
anchor1	This parameter is the start point of the first line.
dir1	This value is the direction of the first line from anchor1.
anchor2	This parameter is the start point of the second line.
dir2	This value is the direction of the second line from anchor2.

Returns

The return value is a vector representing the intersection of the two lines. If the lines do not intersect, the behavior differs based on whether a tolerance is specified. If no tolerance is given, the return value represents the midpoint of the points on each line closest to the other line. If the two lines are parallel, the return value will be the midpoint of the two anchor points. If a tolerance is given and the two lines do not intersect or cross within the given tolerance, an error is raised. Otherwise, the return value is the same as if no tolerance was specified.

Example

Code

# Intersect two lines at 90 degrees
set iPt [pwu::Vector3 intersect {0 0 0} {1 0 0} {1 -1 0} {0 1 0}]
puts $iPt
# Intersect two lines at 90 degrees in different planes
set iPt [pwu::Vector3 intersect {0 0 0} {1 0 0} {1 -1 1} {0 1 0}]
puts $iPt
# Fail to intersect two lines within a given tolerance
catch {pwu::Vector3 intersect -tolerance 0.1 {0 0 0} {1 0 0} \
   {1 -1 1} {0 1 0}} msg
puts $msg
# Try to intersect two parallel lines with no tolerance
set iPt [pwu::Vector3 intersect {0 0 0} {1 0 0} {0 -1 0} {1 0 0}]
puts $iPt
# Try to intersect two parallel lines with a tolerance
catch {pwu::Vector3 intersect -tolerance 0.1 {0 0 0} {1 0 0} \
   {0 -1 0} {1 0 0}} msg
puts $msg

Output

1.0 0.0 0.0
1.0 0.0 0.5
ERROR: Lines do not intersect within the given tolerance.

0.0 -0.5 0.0
ERROR: Lines are parallel.

pwu::Vector3 zero

Return the 3 dimensional zero vector

pwu::Vector3 set x y z

Return a vector with the given x, y and z components

pwu::Vector3 index vec i

Return the value of the vector at the given index

pwu::Vector3 x vec

Return the x component of the vector

pwu::Vector3 y vec

Return the y component of the vector

pwu::Vector3 z vec

Return the z component of the vector

pwu::Vector3 equal ?-tolerance tol? vec1 vec2

Check if two vectors are equal

pwu::Vector3 notEqual ?-tolerance tol? vec1 vec2

Check if two vectors are not equal

pwu::Vector3 add vec1 vec2

Add two vectors together and return the result

pwu::Vector3 subtract vec1 vec2

Subtract one vector from another and return the result

pwu::Vector3 negate vec

Return the negation of a vector

pwu::Vector3 scale vec scalar

Scale a vector by a single scalar value

pwu::Vector3 divide vec scalar

Scale a vector by inverse of a single scalar value

pwu::Vector3 multiply vec1 vec2

Return a vector that is the components of two vectors multiplied together

pwu::Vector3 cross vec1 vec2

Return the cross product of two vectors

pwu::Vector3 dot vec1 vec2

Calculate the dot product of two vectors

pwu::Vector3 normalize ?-length lenVar? vec

Return the normalization of a vector

pwu::Vector3 length vec

Return the length of the vector

pwu::Vector3 distanceToLine vec pt dir

Return the distance of the vector to a line

pwu::Vector3 minimum vec1 vec2

Return a vector that has the minimum components of two vectors

pwu::Vector3 maximum vec1 vec2

Return a vector that has the maximum components of two vectors

pwu::Vector3 affine s vec1 vec2

Return a vector that is the affine combination of two vectors

pwu::Vector3 barycentric pt vec1 vec2 vec3

Return a vector that has the barycentric coordinates of the given point in the frame of the given three vectors

pwu::Vector3 intersect ?-tolerance tol? anchor1 dir1 anchor2 dir2

Return a vector that is the intersection of the two lines specified as two point and direction pairs.