Some minor fixes
Fixed som wrong spellings in cooments, reordering some arguments to be mor uniform, and fixed a small bug in isUniform for 3d matrix.
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ventor3000
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2 changed files with 59 additions and 40 deletions
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@ -17,7 +17,8 @@ import times
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## the translation part of matrix is ignored. The coordinate system used is
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## right handed, because its compatible with 2d coordinate system (rotation around
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## zaxis equals 2d rotation).
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## Operators `+` , `-` , `*` , `/` , `+=` , `-=` , `*=` and `/=` are implemented for vectors and scalars.
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## Operators `+` , `-` , `*` , `/` , `+=` , `-=` , `*=` and `/=` are implemented
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## for vectors and scalars.
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##
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##
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## Quick start example:
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@ -37,7 +38,7 @@ import times
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##
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## var pt2:TPoint3d=pt & m #concatenates pt with m and returns a new point
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##
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## var vec2:TVector3d=vec & m #concatenates vec with m and returns a new vector
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## var vec2:TVector3d=vec & m #concatenates vec with m and returns a new vector
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@ -69,6 +70,7 @@ proc matrix3d*(ax,ay,az,aw,bx,by,bz,bw,cx,cy,cz,cw,tx,ty,tz,tw:float):TMatrix3d
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## Creates a new 4x4 3d transformation matrix.
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## `ax` , `ay` , `az` is the local x axis.
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## `bx` , `by` , `bz` is the local y axis.
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## `cx` , `cy` , `cz` is the local z axis.
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## `tx` , `ty` , `tz` is the translation.
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proc vector3d*(x,y,z:float):TVector3d {.noInit,inline.}
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## Returns a new 3d vector (`x`,`y`,`z`)
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@ -114,14 +116,19 @@ proc safeArccos(v:float):float=
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template makeBinOpVector(s:expr)=
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## implements binary operators + , - , * and / for vectors
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proc s*(a,b:TVector3d):TVector3d {.inline,noInit.} = vector3d(s(a.x,b.x),s(a.y,b.y),s(a.z,b.z))
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proc s*(a:TVector3d,b:float):TVector3d {.inline,noInit.} = vector3d(s(a.x,b),s(a.y,b),s(a.z,b))
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proc s*(a:float,b:TVector3d):TVector3d {.inline,noInit.} = vector3d(s(a,b.x),s(a,b.y),s(a,b.z))
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proc s*(a,b:TVector3d):TVector3d {.inline,noInit.} =
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vector3d(s(a.x,b.x),s(a.y,b.y),s(a.z,b.z))
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proc s*(a:TVector3d,b:float):TVector3d {.inline,noInit.} =
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vector3d(s(a.x,b),s(a.y,b),s(a.z,b))
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proc s*(a:float,b:TVector3d):TVector3d {.inline,noInit.} =
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vector3d(s(a,b.x),s(a,b.y),s(a,b.z))
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template makeBinOpAssignVector(s:expr)=
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## implements inplace binary operators += , -= , /= and *= for vectors
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proc s*(a:var TVector3d,b:TVector3d) {.inline.} = s(a.x,b.x) ; s(a.y,b.y) ; s(a.z,b.z)
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proc s*(a:var TVector3d,b:float) {.inline.} = s(a.x,b) ; s(a.y,b) ; s(a.z,b)
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proc s*(a:var TVector3d,b:TVector3d) {.inline.} =
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s(a.x,b.x) ; s(a.y,b.y) ; s(a.z,b.z)
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proc s*(a:var TVector3d,b:float) {.inline.} =
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s(a.x,b) ; s(a.y,b) ; s(a.z,b)
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@ -235,7 +242,7 @@ proc rotate*(angle:float,axis:TVector3d):TMatrix3d {.noInit.}=
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uwomc+vsi, vwomc-usi, w2+(1.0-w2)*cs, 0.0,
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0.0,0.0,0.0,1.0)
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proc rotate*(angle:float,axis:TVector3d,org:TPoint3d):TMatrix3d {.noInit.}=
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proc rotate*(angle:float,org:TPoint3d,axis:TVector3d):TMatrix3d {.noInit.}=
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## Creates a rotation matrix that rotates `angle` radians over
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## `axis`, which passes through `org`.
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@ -319,7 +326,10 @@ proc isUniform*(m:TMatrix3d,tol=1.0e-6):bool=
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## and perpendicular comparison.
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#dot product=0 means perpendicular coord. system, check xaxis vs yaxis and xaxis vs zaxis
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if abs(m.ax*m.bx+m.ay*m.by+m.az*m.bz)<=tol and abs(m.ax*m.cx+m.ay*m.cy+m.az*m.cz)<=tol:
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if abs(m.ax*m.bx+m.ay*m.by+m.az*m.bz)<=tol and # x vs y
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abs(m.ax*m.cx+m.ay*m.cy+m.az*m.cz)<=tol and #x vs z
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abs(m.bx*m.cx+m.by*m.cy+m.bz*m.cz)<=tol: #y vs z
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#subtract squared lengths of axes to check if uniform scaling:
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let
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sqxlen=(m.ax*m.ax+m.ay*m.ay+m.az*m.az)
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@ -355,7 +365,7 @@ proc mirror*(planeperp:TVector3d):TMatrix3d {.noInit.}=
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0,0,0,1)
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proc mirror*(planeperp:TVector3d,org:TPoint3d):TMatrix3d {.noInit.}=
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proc mirror*(org:TPoint3d,planeperp:TVector3d):TMatrix3d {.noInit.}=
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## Creates a matrix that mirrors over the plane that has `planeperp` as normal,
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## and passes through `org`. `planeperp` does not need to be normalized.
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@ -393,7 +403,8 @@ proc mirror*(planeperp:TVector3d,org:TPoint3d):TMatrix3d {.noInit.}=
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proc determinant*(m:TMatrix3d):float=
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## Computes the determinant of matrix `m`.
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# This computation is gotten from ratsimp(optimize(determinant(m))) in maxima CAS
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# This computation is gotten from ratsimp(optimize(determinant(m)))
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# in maxima CAS
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let
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O1=m.cx*m.tw-m.cw*m.tx
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O2=m.cy*m.tw-m.cw*m.ty
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@ -537,7 +548,7 @@ proc len*(v:TVector3d):float=
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proc `len=`*(v:var TVector3d,newlen:float) {.noInit.} =
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## Sets the length of the vector, keeping its direction.
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## If the vector has zero length before chenging it's length,
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## If the vector has zero length before changing it's length,
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## an arbitrary vector of the requested length is returned.
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let fac=newlen/v.len
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@ -702,8 +713,7 @@ proc stretch*(v:var TVector3d,sx,sy,sz:float)=
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proc mirror*(v:var TVector3d,planeperp:TVector3d)=
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## Computes the mirrored vector of `v` over the plane
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## that has `planeperp` as normal direction. This is the
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## same as reflecting the vector `v` on the plane.
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## that has `planeperp` as normal direction.
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## `planeperp` does not need to be normalized.
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var n=planeperp
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@ -750,7 +760,8 @@ proc cross*(v1,v2:TVector3d):TVector3d {.inline.}=
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## Computes the cross product of two vectors.
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## The result is a vector which is perpendicular
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## to the plane of `v1` and `v2`, which means
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## cross(xaxis,yaxis)=zaxis
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## cross(xaxis,yaxis)=zaxis. The magnitude of the result is
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## zero if the vectors are colinear.
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result.x = (v1.y * v2.z) - (v2.y * v1.z)
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result.y = (v1.z * v2.x) - (v2.z * v1.x)
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result.z = (v1.x * v2.y) - (v2.x * v1.y)
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@ -798,16 +809,16 @@ proc arbitraryAxis*(norm:TVector3d):TMatrix3d {.noInit.}=
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0.0,0.0,0.0,1.0)
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proc bisect*(v1,v2:TVector3d):TVector3d {.noInit.}=
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## Computes the bisector between v1 and v2 as a normalized vector
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## If one of the input vectors has zero length, a normalized verison
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## Computes the bisector between v1 and v2 as a normalized vector.
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## If one of the input vectors has zero length, a normalized version
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## of the other is returned. If both input vectors has zero length,
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## an arbitrary normalized vector is returned.
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## an arbitrary normalized vector `v1`is returned.
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var
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vmag1=v1.len
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vmag2=v2.len
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# zero length vector equals arbitrary vector, just change to magnitude to one to
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# avoid zero division
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# zero length vector equals arbitrary vector, just change
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# magnitude to one to avoid zero division
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if vmag1==0.0:
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if vmag2==0: #both are zero length return any normalized vector
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return XAXIS
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@ -943,7 +954,7 @@ proc rotate*(p:var TPoint3d,rad:float,axis:TVector3d)=
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p.y=v.y
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p.z=v.z
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proc rotate*(p:var TPoint3d,angle:float,axis:TVector3d,org:TPoint3d)=
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proc rotate*(p:var TPoint3d,angle:float,org:TPoint3d,axis:TVector3d)=
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## Rotates point `p` in place `rad` radians about an axis
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## passing through `org`
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@ -994,13 +1005,15 @@ proc scale*(p:var TPoint3d,fac:float,org:TPoint3d){.inline.}=
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p.z=(p.z - org.z) * fac + org.z
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proc stretch*(p:var TPoint3d,facx,facy,facz:float){.inline.}=
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## Scales a point in place non uniformly `facx` and `facy` times with world origo as origin.
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## Scales a point in place non uniformly `facx` , `facy` , `facz` times
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## with world origo as origin.
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p.x*=facx
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p.y*=facy
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p.z*=facz
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proc stretch*(p:var TPoint3d,facx,facy,facz:float,org:TPoint3d){.inline.}=
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## Scales the point in place non uniformly `facx` and `facy` times with `org` as origin.
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## Scales the point in place non uniformly `facx` , `facy` , `facz` times
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## with `org` as origin.
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p.x=(p.x - org.x) * facx + org.x
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p.y=(p.y - org.y) * facy + org.y
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p.z=(p.z - org.z) * facz + org.z
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