Difference between revisions of "Category:Physics Engine/Vectors"

A vector is a 2-dimensional object with x and y components. Its type is TI.cpVect.  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">vector = physics.Vect(x, y)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| x  

| '''in''' number  

| The _x_ component of the vector

| y  

| '''in''' number  

| The _y_ component of the vector

| angle  

| '''in''' number  

| An angle in radians

| vect  

| '''in''' physics.Vect  

| A vector

| vector  

| '''out''' physics.Vect  

| A vector

|}

<!-- table end -->  

<br> Creates a vector with initial x and y component values. The second form creates a unit vector pointing in direction ''angle''. The third form creates a copy of the input vector.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">sum = physics.Vect:add(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| A vector to add to ''self''

| sum  

| '''out''' physics.Vect  

| The vector sum of ''self'' and ''vec''

|}

<!-- table end -->  

The Vect class also implements the addition operator (+). Therefore vectors ''v1'' and ''v2'' can be added with the expression ''v1'' + ''v2''.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">clamped = physics.Vect:clamp(len)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| len  

| '''in''' number  

| The maximum length of the vector

| clamped  

| '''out''' physics.Vect  

| A new vector with a length no longer than ''len''

|}

<!-- table end -->  

<br> Returns a copy of ''self'' clamped to length ''len''.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">crossprod = physics.Vect:cross(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| The vector to cross with ''self''

| zmag  

| '''out''' number  

| The z magnitude of the cross product of ''self'' and ''vec''

|}

<!-- table end -->  

<br> Returns the z magnitude of the cross product of ''self'' and ''vec''.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">dist = physics.Vect:dist(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| The vector to which to find the distance from ''self''

| dist  

| '''out''' number  

| The distance from ''self'' to ''vec''

|}

<!-- table end -->  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">distsq = physics.Vect:distsq(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| The vector to which to find the distance squared from ''self''

| distsq  

| '''out''' number  

| The distance squared from ''self'' to ''vec''

|}

<!-- table end -->  

<br> Returns the distance squared between ''self'' and ''vec''. This routine is faster than physics.Vect:dist when you only need to compare distances.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">dotprod = physics.Vect:dot(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| The other vector

| dotprod  

| '''out''' number  

| The scalar dot product of ''self'' and ''vec''

|}

<!-- table end -->  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">isequ = physics.Vect:eql(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| The vector against which to compare with ''self''

| isequ  

| '''out''' boolean  

| True if the components of ''self'' equal the components of ''vec''

|}

<!-- table end -->  

The Vect class also implements the equal comparison operator (==). Therefore vectors ''v1'' and ''v2'' can be compared with the expression ''v1'' == ''v2''.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">len = physics.Vect:length()

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| len  

| '''out''' number  

| The length of vector ''self''

|}

<!-- table end -->  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">lensq = physics.Vect:lengthsq()

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| lensq  

| '''out''' number  

| The length squared of vector ''self''

|}

<!-- table end -->  

<br> Returns the length squared of ''self''. This routine is faster than Vect:length() when you only need to compare lengths.  

Introduced in platform.apiLevel = '2.0'  

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

| self

| '''in''' physics.Vect  

| The input vector

| vec

| '''in''' physics.Vect

| The other vector

| f

| '''in''' number

| ''f_ is a fractional number from 0 to 1 representing the proportion of distance between _self'' and ''vec''

| v

| A vector interpolated between ''self'' and ''vec''

<!-- table end -->  

<br> Returns the linear interpolation between ''self'' and ''vec'' as a vector. ''f_ is the fraction of distance between _self'' and ''vec''.

<br>  

Introduced in platform.apiLevel = '2.0'  

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

| self

| '''in''' physics.Vect  

| The input vector

| vec

| '''in''' physics.Vect

| The other vector

| d

| '''in''' number

| The distance from ''self'' to ''vec'' to interpolate a new vector

| v

| '''out''' physics.Vect

<!-- table end -->  

<br> Returns a vector interpolated from ''self'' towards ''vec'' with length _d_.

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">v = physics.Vect:mult(factor)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| factor  

| '''in''' number  

| The value to multiply by ''self''

| v  

| '''out''' physics.Vect  

| The resulting scaled vector

|}

<!-- table end -->  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">isnear = physics.Vect:near(vec, distance)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| The value to multiply by ''self''

| distance  

| '''in''' number  

| The distance from ''vec''

| isnear  

| '''out''' boolean  

| True if ''self'' is within ''distance'' of ''vec''

|}

<!-- table end -->  

<br> Determines if ''self'' is near another vector.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">v = physics.Vect:neg()

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| v  

| '''out''' physics.Vect  

| The resulting negated vector

|}

<!-- table end -->  

<br> Returns the negative of ''self''.  

The Vect class also implements the unary minus operator (<nowiki>-</nowiki>''self'').  

Introduced in platform.apiLevel = '2.0'  

===== normalize =====

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">normvec = physics.Vect:normalize()

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| normvec  

| '''out''' physics.Vect  

| The resulting normalized vector

|}

<!-- table end -->  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">normvec = physics.Vect:normalizeSafe()

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| normvec  

| '''out''' physics.Vect  

| The resulting normalized vector

|}

<!-- table end -->  

<br> Returns a normalized copy of ''self''. Protects against division by zero.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">perpvec = physics.Vect:perp()

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| perpvec  

| '''out''' physics.Vect  

| The resulting perpendicular vector

|}

<!-- table end -->  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">pvec = physics.Vect:project(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| The other vector

| pvec  

| '''out''' physics.Vect  

| The vector of ''self'' projected onto ''vec''

|}

<!-- table end -->  

<br> Computes the projection of ''self'' onto another vector.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">rvec = physics.Vect:rotate(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| The other vector

| rvec  

| '''out''' physics.Vect  

| The resulting rotated vector

|}

<!-- table end -->  

<br> Uses complex multiplication to rotate ''self'' by ''vec''. Scaling will occur if ''self'' is not a unit vector.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">perpvec = physics.Vect:rperp()

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| perpvec  

| '''out''' physics.Vect  

| The resulting perpendicular vector

|}

<!-- table end -->  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">self = physics.Vect:setx(x)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The vector to modify

| x  

| '''in''' number  

| The new value of the _x_ component of the vector

| self  

| '''out''' physics.Vect  

| The input vector is returned as the output

|}

<!-- table end -->  

<br> Changes the value of the ''x_ component of _self''. Returns ''self''.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">self = physics.Vect:sety(y)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The vector to modify

| y  

| '''in''' number  

| The new value of the _y_ component of the vector

| self  

| '''out''' physics.Vect  

| The input vector is returned as the output

|}

<!-- table end -->  

<br> Changes the value of the ''y_ component of _self''. Returns ''self''.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">v = physics.Vect:slerp(vec, f)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| A unit vector

| vec  

| '''in''' physics.Vect  

| The other unit vector

| f  

| '''in''' number  

| ''f_ is a fractional number from 0 to 1 representing the proportion of distance between _self'' and ''vec''

| v  

| '''out''' physics.Vect  

| A vector interpolated between ''self'' and ''vec''

|}

<!-- table end -->  

<br> Computes a spherical linear interpolation between unit vectors ''self'' and ''vec''.  

|}

<br> <!-- code start-->  

===== physics.Vect:slerp  =====

----

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">local vect1 = physics.Vect(math.pi/3) -- unit vector with angle pi/3 radians

</pre><!-- code end--> <div style="white-space: pre">

 

</div>  

| <span style="color:#AAAA00">'''NOTE''':</span> '''Notes'''  

----

<br>  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">v = physics.Vect:slerpconst(vec, angle)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| A unit vector

| vec  

| '''in''' physics.Vect  

| The other unit vector

| angle  

| '''in''' number  

| The maximum angle between ''self'' and ''vec'' to interpolate a new vector

| v  

| '''out''' physics.Vect  

|  

|}

<!-- table end -->  

<br> Returns the spherical linear interpolation from ''self'' towards ''vec'' but by no more than ''angle'' in radians.  

|}

This routine computes meaningful results only when the two inputs are unit vectors.  

</div>  

| <span style="color:#AAAA00">'''NOTE''':</span> '''NOTE'''  

----

 

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">diff = physics.Vect:sub(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| A vector to subtract from ''self''

| diff  

| '''out''' physics.Vect  

| The vector difference between ''self'' and ''vec''

|}

<!-- table end -->  

The Vect class also implements the subtraction operator (-). Therefore vector ''v2'' can be subtracted from ''v1'' with the expression ''v1'' <nowiki>-</nowiki> ''v2''.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">angle = physics.Vect:toangle()

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| angle  

| '''out''' number  

| The angle of ''self''

|}

<!-- table end -->  

<br> Returns the angle in radians of ''self''.  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">uvec = physics.Vect:unrotate(vec)

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| vec  

| '''in''' physics.Vect  

| The other vector

| uvec  

| '''out''' physics.Vect  

| The resulting unrotated vector

|}

<!-- table end -->  

Introduced in platform.apiLevel = '2.0'  

<!-- code start-->  

<pre style="margin-left:20px; font-size:1.4em; background-color:#fdfdfd">x = physics.Vect:x()

</pre><!-- code end--> <!-- table start -->  

{| border="1" width="100%" cellspacing="0" cellpadding="4" style="border-color:#eee" class="wikitable sortable"

|-

! Parameter  

! Type  

! Description <!-- header row end -->

| self  

| '''in''' physics.Vect  

| The input vector

| x  

| '''out''' number