diff options
Diffstat (limited to 'lib/pure/basic2d.nim')
| -rw-r--r-- | lib/pure/basic2d.nim | 135 |
1 files changed, 68 insertions, 67 deletions
diff --git a/lib/pure/basic2d.nim b/lib/pure/basic2d.nim index 9c327a011..bb2af79c6 100644 --- a/lib/pure/basic2d.nim +++ b/lib/pure/basic2d.nim @@ -32,7 +32,7 @@ import strutils ## ## var pt2:TPoint2d=pt & m #concatenates pt with m and returns a new point ## -## var vec2:TVEctor2d=vec & m #concatenates vec with m and returns a new vector +## var vec2:TVector2d=vec & m #concatenates vec with m and returns a new vector const @@ -113,13 +113,13 @@ proc safeArccos(v:float):float= return arccos(clamp(v,-1.0,1.0)) -template makeBinOpVector*(s:expr)= +template makeBinOpVector(s:expr)= ## implements binary operators + , - , * and / for vectors proc s*(a,b:TVector2d):TVector2d {.inline,noInit.} = vector2d(s(a.x,b.x),s(a.y,b.y)) proc s*(a:TVector2d,b:float):TVector2d {.inline,noInit.} = vector2d(s(a.x,b),s(a.y,b)) proc s*(a:float,b:TVector2d):TVector2d {.inline,noInit.} = vector2d(s(a,b.x),s(a,b.y)) -template makeBinOpAssignVector*(s:expr)= +template makeBinOpAssignVector(s:expr)= ## implements inplace binary operators += , -= , /= and *= for vectors proc s*(a:var TVector2d,b:TVector2d) {.inline.} = s(a.x,b.x) ; s(a.y,b.y) proc s*(a:var TVector2d,b:float) {.inline.} = s(a.x,b) ; s(a.y,b) @@ -312,6 +312,17 @@ proc isIdentity*(m:TMatrix2d,tol=1.0e-6):bool= ## using `tol` as tolerance for each element. return equals(m,IDMATRIX,tol) +proc apply*(m:TMatrix2d,x,y:var float,translate=false)= + ## Applies transformation `m` onto `x`,`y`, optionally + ## using the translation part of the matrix. + if translate: # positional style transform + let newx=x*m.ax+y*m.bx+m.tx + y=x*m.ay+y*m.by+m.ty + x=newx + else: # delta style transform + let newx=x*m.ax+y*m.bx + y=x*m.ay+y*m.by + x=newx @@ -421,11 +432,10 @@ proc normalize*(v:var TVector2d) {.inline.}= raise newException(EDivByZero,"Cannot normalize zero length vector") proc transformNorm*(v:var TVector2d,t:TMatrix2d)= - ## Applies transformation `m` onto `v` in place, assuming `v` is a normal. - ## The length of the resulting vector is undefined, - ## but most likely not the same as the input vector. - ## If the matrix is not invertible (determinant=0), an EDivByZero - ## will be raised. + ## Applies a normal direction transformation `t` onto `v` in place. + ## The resulting vector is *not* normalized. Transforming a vector ignores the + ## translational part of the matrix. If the matrix is not invertible + ## (determinant=0), an EDivByZero will be raised. # transforming a normal is done by transforming # by the transpose of the inverse of the original matrix @@ -456,11 +466,11 @@ proc transformInv*(v:var TVector2d,t:TMatrix2d)= v.x = newx proc transformNormInv*(v:var TVector2d,t:TMatrix2d)= - ## Applies inverse of a transformation `m` to `v` in place, - ## assuming `v` is a normal. This is faster than creating an inverse + ## Applies an inverse normal direction transformation `t` onto `v` in place. + ## This is faster than creating an inverse ## matrix and transformNorm(...) it. Transforming a vector ignores the ## translational part of the matrix. - + # normal inverse transform is done by transforming # by the inverse of the transpose of the inverse of the org. matrix # which is equivalent with transforming with the transpose. @@ -596,6 +606,41 @@ proc turnAngle*(v1,v2:TVector2d):float= return -a return a +proc bisect*(v1,v2:TVector2d):TVector2d {.noInit.}= + ## Computes the bisector between v1 and v2 as a normalized vector. + ## If one of the input vectors has zero length, a normalized verison + ## of the other is returned. If both input vectors has zero length, + ## an arbitrary normalized vector is returned. + var + vmag1=v1.len + vmag2=v2.len + + # zero length vector equals arbitrary vector, just change to magnitude to one to + # avoid zero division + if vmag1==0.0: + if vmag2==0: #both are zero length return any normalized vector + return XAXIS + vmag1=1.0 + if vmag2==0.0: vmag2=1.0 + + let + x1=v1.x/vmag1 + y1=v1.y/vmag1 + x2=v2.x/vmag2 + y2=v2.y/vmag2 + + result.x=(x1 + x2) * 0.5 + result.y=(y1 + y2) * 0.5 + + if not result.tryNormalize(): + # This can happen if vectors are colinear. In this special case + # there are actually two bisectors, we select just + # one of them (x1,y1 rotated 90 degrees ccw). + result.x = -y1 + result.y = x1 + + + # *************************************** # TPoint2d implementation # *************************************** @@ -729,17 +774,17 @@ proc scale*(p:var TPoint2d,fac:float) {.inline.}= proc scale*(p:var TPoint2d,fac:float,org:TPoint2d){.inline.}= ## Scales the point in place `fac` times with `org` as origin. p.x=(p.x - org.x) * fac + org.x - p.y=(p.x - org.y) * fac + org.y + p.y=(p.y - org.y) * fac + org.y proc stretch*(p:var TPoint2d,facx,facy:float){.inline.}= ## Scales a point in place non uniformly `facx` and `facy` times with world origo as origin. p.x*=facx - p.y*=facx + p.y*=facy proc stretch*(p:var TPoint2d,facx,facy:float,org:TPoint2d){.inline.}= ## Scales the point in place non uniformly `facx` and `facy` times with `org` as origin. p.x=(p.x - org.x) * facx + org.x - p.y=(p.x - org.y) * facy + org.y + p.y=(p.y - org.y) * facy + org.y proc move*(p:var TPoint2d,dx,dy:float){.inline.}= ## Translates a point `dx`, `dy` in place. @@ -751,31 +796,15 @@ proc move*(p:var TPoint2d,v:TVector2d){.inline.}= p.x+=v.x p.y+=v.y - -# *************************************** -# Misc. 2d utilities -# *************************************** -proc transform*(x,y:var float,m:TMatrix2d,translate=false)= - ## Concatenates vector x,y with matrix m in place, optionally - ## using the translation part of the matrix. - if translate: # positional style transform - let newx=x*m.ax+y*m.bx+m.tx - y=x*m.ay+y*m.by+m.ty - x=newx - else: # delta style transform - let newx=x*m.ax+y*m.bx - y=x*m.ay+y*m.by - x=newx - proc sgnArea*(a,b,c:TPoint2d):float= - ## Computes the signed area of the triangle a,b,c. + ## Computes the signed area of the triangle thru points `a`,`b` and `c` ## result>0.0 for counter clockwise triangle ## result<0.0 for clockwise triangle ## This is commonly used to determinate side of a point with respect to a line. return ((b.x - c.x) * (b.y - a.y)-(b.y - c.y) * (b.x - a.x))*0.5 proc area*(a,b,c:TPoint2d):float= - ## Computes the area of the triangle a,b,c + ## Computes the area of the triangle thru points `a`,`b` and `c` return abs(sgnArea(a,b,c)) proc closestPoint*(p:TPoint2d,pts:varargs[TPoint2d]):TPoint2d= @@ -795,6 +824,11 @@ proc closestPoint*(p:TPoint2d,pts:varargs[TPoint2d]):TPoint2d= result=pts[bestidx] + +# *************************************** +# Misc. math utilities that should +# probably be in another module. +# *************************************** proc normAngle*(ang:float):float= ## Returns an angle in radians, that is equal to `ang`, ## but in the range 0 to <2*PI @@ -803,45 +837,12 @@ proc normAngle*(ang:float):float= return ang mod DEG360 -proc degToRad*(deg:float):float= +proc degToRad*(deg:float):float {.inline.}= ## converts `deg` degrees to radians deg / RAD2DEGCONST -proc radToDeg*(rad:float):float= +proc radToDeg*(rad:float):float {.inline.}= ## converts `rad` radians to degrees rad * RAD2DEGCONST -proc bisect*(v1,v2:TVector2d):TVector2d {.noInit.}= - ## Computes the bisector between v1 and v2 as a normalized vector - ## If one of the input vectors has zero length, a normalized verison - ## of the other is returned. - ## If both input vectors has zero length, an arbitrary normalized vector - ## is returned. - var - vmag1=v1.len - vmag2=v2.len - - # zero length vector equals arbitrary vector, just change to magnitude to one to - # avoid zero division - if vmag1==0.0: - if vmag2==0: #both are zero length return any normalized vector - return XAXIS - vmag1=1.0 - if vmag2==0.0: vmag2=1.0 - - let - x1=v1.x/vmag1 - y1=v1.y/vmag1 - x2=v2.x/vmag2 - y2=v2.y/vmag2 - - result.x=(x1 + x2) * 0.5 - result.y=(y1 + y2) * 0.5 - - if not result.tryNormalize(): - # This can happen if vectors are colinear. In this special case - # there are actually two bisectors, we select just - # one of them (x1,y1 rotated 90 degrees ccw). - result.x = -y1 - result.y = x1 \ No newline at end of file |