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This commit is contained in:
Adam Strzelecki
@@ -13,26 +13,26 @@ import strutils
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## Basic 2d support with vectors, points, matrices and some basic utilities.
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## Vectors are implemented as direction vectors, ie. when transformed with a matrix
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## the translation part of matrix is ignored.
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## the translation part of matrix is ignored.
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## Operators `+` , `-` , `*` , `/` , `+=` , `-=` , `*=` and `/=` are implemented for vectors and scalars.
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##
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## Quick start example:
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##
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##
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## # Create a matrix which first rotates, then scales and at last translates
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##
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##
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## var m:Matrix2d=rotate(DEG90) & scale(2.0) & move(100.0,200.0)
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##
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##
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## # Create a 2d point at (100,0) and a vector (5,2)
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##
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## var pt:Point2d=point2d(100.0,0.0)
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##
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##
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## var pt:Point2d=point2d(100.0,0.0)
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##
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## var vec:Vector2d=vector2d(5.0,2.0)
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##
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##
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##
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##
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## pt &= m # transforms pt in place
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##
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##
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## var pt2:Point2d=pt & m #concatenates pt with m and returns a new point
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##
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##
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## var vec2:Vector2d=vec & m #concatenates vec with m and returns a new vector
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@@ -64,12 +64,12 @@ type
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## not used for geometric transformations in 2d.
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ax*,ay*,bx*,by*,tx*,ty*:float
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Point2d* = object
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## Implements a non-homogeneous 2d point stored as
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## Implements a non-homogeneous 2d point stored as
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## an `x` coordinate and an `y` coordinate.
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x*,y*:float
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Vector2d* = object
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## Implements a 2d **direction vector** stored as
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## an `x` coordinate and an `y` coordinate. Direction vector means,
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Vector2d* = object
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## Implements a 2d **direction vector** stored as
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## an `x` coordinate and an `y` coordinate. Direction vector means,
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## that when transforming a vector with a matrix, the translational
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## part of the matrix is ignored.
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x*,y*:float
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@@ -78,7 +78,7 @@ type
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# Some forward declarations...
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proc matrix2d*(ax,ay,bx,by,tx,ty:float):Matrix2d {.noInit.}
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## Creates a new matrix.
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## Creates a new matrix.
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## `ax`,`ay` is the local x axis
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## `bx`,`by` is the local y axis
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## `tx`,`ty` is the translation
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@@ -99,7 +99,7 @@ let
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YAXIS*:Vector2d=vector2d(0.0,1.0)
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## Quick acces to an 2d y-axis unit vector
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# ***************************************
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# Private utils
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# ***************************************
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@@ -114,13 +114,13 @@ proc safeArccos(v:float):float=
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return arccos(clamp(v,-1.0,1.0))
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template makeBinOpVector(s:expr)=
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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:Vector2d):Vector2d {.inline,noInit.} = vector2d(s(a.x,b.x),s(a.y,b.y))
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proc s*(a:Vector2d,b:float):Vector2d {.inline,noInit.} = vector2d(s(a.x,b),s(a.y,b))
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proc s*(a:float,b:Vector2d):Vector2d {.inline,noInit.} = vector2d(s(a,b.x),s(a,b.y))
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template makeBinOpAssignVector(s:expr)=
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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 Vector2d,b:Vector2d) {.inline.} = s(a.x,b.x) ; s(a.y,b.y)
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proc s*(a:var Vector2d,b:float) {.inline.} = s(a.x,b) ; s(a.y,b)
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@@ -144,7 +144,7 @@ proc matrix2d*(ax,ay,bx,by,tx,ty:float):Matrix2d =
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proc `&`*(a,b:Matrix2d):Matrix2d {.noInit.} = #concatenate matrices
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## Concatenates matrices returning a new matrix.
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# | a.AX a.AY 0 | | b.AX b.AY 0 |
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# | a.BX a.BY 0 | * | b.BX b.BY 0 |
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# | a.TX a.TY 1 | | b.TX b.TY 1 |
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@@ -153,7 +153,7 @@ proc `&`*(a,b:Matrix2d):Matrix2d {.noInit.} = #concatenate matrices
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a.ax * b.ay + a.ay * b.by,
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a.bx * b.ax + a.by * b.bx,
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a.bx * b.ay + a.by * b.by,
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a.tx * b.ax + a.ty * b.bx + b.tx,
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a.tx * b.ax + a.ty * b.bx + b.tx,
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a.tx * b.ay + a.ty * b.by + b.ty)
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@@ -169,13 +169,13 @@ proc stretch*(sx,sy:float):Matrix2d {.noInit.} =
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## Returns new a stretch matrix, which is a
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## scale matrix with non uniform scale in x and y.
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result.setElements(sx,0,0,sy,0,0)
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proc stretch*(sx,sy:float,org:Point2d):Matrix2d {.noInit.} =
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## Returns a new stretch matrix, which is a
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## scale matrix with non uniform scale in x and y.
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## `org` is used as stretch origin.
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result.setElements(sx,0,0,sy,org.x-sx*org.x,org.y-sy*org.y)
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proc move*(dx,dy:float):Matrix2d {.noInit.} =
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## Returns a new translation matrix.
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result.setElements(1,0,0,1,dx,dy)
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@@ -187,7 +187,7 @@ proc move*(v:Vector2d):Matrix2d {.noInit.} =
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proc rotate*(rad:float):Matrix2d {.noInit.} =
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## Returns a new rotation matrix, which
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## represents a rotation by `rad` radians
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let
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let
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s=sin(rad)
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c=cos(rad)
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result.setElements(c,s,-s,c,0,0)
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@@ -200,7 +200,7 @@ proc rotate*(rad:float,org:Point2d):Matrix2d {.noInit.} =
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s=sin(rad)
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c=cos(rad)
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result.setElements(c,s,-s,c,org.x+s*org.y-c*org.x,org.y-c*org.y-s*org.x)
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proc mirror*(v:Vector2d):Matrix2d {.noInit.} =
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## Returns a new mirror matrix, mirroring
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## around the line that passes through origo and
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@@ -211,7 +211,7 @@ proc mirror*(v:Vector2d):Matrix2d {.noInit.} =
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nd=1.0/(sqx+sqy) #used to normalize invector
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xy2=v.x*v.y*2.0*nd
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sqd=nd*(sqx-sqy)
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if nd==Inf or nd==NegInf:
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return IDMATRIX #mirroring around a zero vector is arbitrary=>just use identity
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@@ -230,7 +230,7 @@ proc mirror*(org:Point2d,v:Vector2d):Matrix2d {.noInit.} =
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nd=1.0/(sqx+sqy) #used to normalize invector
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xy2=v.x*v.y*2.0*nd
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sqd=nd*(sqx-sqy)
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if nd==Inf or nd==NegInf:
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return IDMATRIX #mirroring around a zero vector is arbitrary=>just use identity
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@@ -238,47 +238,47 @@ proc mirror*(org:Point2d,v:Vector2d):Matrix2d {.noInit.} =
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sqd,xy2,
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xy2,-sqd,
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org.x-org.y*xy2-org.x*sqd,org.y-org.x*xy2+org.y*sqd)
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proc skew*(xskew,yskew:float):Matrix2d {.noInit.} =
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## Returns a new skew matrix, which has its
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## Returns a new skew matrix, which has its
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## x axis rotated `xskew` radians from the local x axis, and
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## y axis rotated `yskew` radians from the local y axis
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result.setElements(cos(yskew),sin(yskew),-sin(xskew),cos(xskew),0,0)
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proc `$`* (t:Matrix2d):string {.noInit.} =
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## Returns a string representation of the matrix
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return rtos(t.ax) & "," & rtos(t.ay) &
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"," & rtos(t.bx) & "," & rtos(t.by) &
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"," & rtos(t.bx) & "," & rtos(t.by) &
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"," & rtos(t.tx) & "," & rtos(t.ty)
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proc isUniform*(t:Matrix2d,tol=1.0e-6):bool=
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## Checks if the transform is uniform, that is
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## Checks if the transform is uniform, that is
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## perpendicular axes of equal length, which means (for example)
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## it cannot transform a circle into an ellipse.
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## `tol` is used as tolerance for both equal length comparison
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## `tol` is used as tolerance for both equal length comparison
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## and perp. comparison.
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#dot product=0 means perpendicular coord. system:
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if abs(t.ax*t.bx+t.ay*t.by)<=tol:
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if abs(t.ax*t.bx+t.ay*t.by)<=tol:
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#subtract squared lengths of axes to check if uniform scaling:
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if abs((t.ax*t.ax+t.ay*t.ay)-(t.bx*t.bx+t.by*t.by))<=tol:
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return true
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return false
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proc determinant*(t:Matrix2d):float=
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## Computes the determinant of the matrix.
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#NOTE: equivalent with perp.dot product for two 2d vectors
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return t.ax*t.by-t.bx*t.ay
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return t.ax*t.by-t.bx*t.ay
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proc isMirroring* (m:Matrix2d):bool=
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## Checks if the `m` is a mirroring matrix,
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## which means it will reverse direction of a curve transformed with it
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return m.determinant<0.0
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proc inverse*(m:Matrix2d):Matrix2d {.noInit.} =
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## Returns a new matrix, which is the inverse of the matrix
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## If the matrix is not invertible (determinant=0), an EDivByZero
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@@ -286,7 +286,7 @@ proc inverse*(m:Matrix2d):Matrix2d {.noInit.} =
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let d=m.determinant
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if d==0.0:
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raise newException(DivByZeroError,"Cannot invert a zero determinant matrix")
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result.setElements(
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m.by/d,-m.ay/d,
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-m.bx/d,m.ax/d,
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@@ -296,14 +296,14 @@ proc inverse*(m:Matrix2d):Matrix2d {.noInit.} =
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proc equals*(m1:Matrix2d,m2:Matrix2d,tol=1.0e-6):bool=
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## Checks if all elements of `m1`and `m2` is equal within
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## a given tolerance `tol`.
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return
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return
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abs(m1.ax-m2.ax)<=tol and
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abs(m1.ay-m2.ay)<=tol and
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abs(m1.bx-m2.bx)<=tol and
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abs(m1.by-m2.by)<=tol and
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abs(m1.tx-m2.tx)<=tol and
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abs(m1.ty-m2.ty)<=tol
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proc `=~`*(m1,m2:Matrix2d):bool=
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## Checks if `m1`and `m2` is approximately equal, using a
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## tolerance of 1e-6.
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@@ -350,16 +350,16 @@ proc slopeVector2d*(slope:float,len:float):Vector2d {.noInit.} =
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proc len*(v:Vector2d):float {.inline.}=
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## Returns the length of the vector.
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sqrt(v.x*v.x+v.y*v.y)
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proc `len=`*(v:var Vector2d,newlen:float) {.noInit.} =
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## Sets the length of the vector, keeping its angle.
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let fac=newlen/v.len
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if newlen==0.0:
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v.x=0.0
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v.y=0.0
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return
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if fac==Inf or fac==NegInf:
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#to short for float accuracy
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#do as good as possible:
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@@ -368,30 +368,30 @@ proc `len=`*(v:var Vector2d,newlen:float) {.noInit.} =
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else:
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v.x*=fac
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v.y*=fac
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proc sqrLen*(v:Vector2d):float {.inline.}=
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## Computes the squared length of the vector, which is
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## faster than computing the absolute length.
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v.x*v.x+v.y*v.y
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proc angle*(v:Vector2d):float=
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## Returns the angle of the vector.
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## Returns the angle of the vector.
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## (The counter clockwise plane angle between posetive x axis and `v`)
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result=arctan2(v.y,v.x)
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if result<0.0: result+=DEG360
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proc `$` *(v:Vector2d):string=
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## String representation of `v`
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result=rtos(v.x)
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result.add(",")
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result.add(rtos(v.y))
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proc `&` *(v:Vector2d,m:Matrix2d):Vector2d {.noInit.} =
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## Concatenate vector `v` with a transformation matrix.
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## Transforming a vector ignores the translational part
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## of the matrix.
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# | AX AY 0 |
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# | X Y 1 | * | BX BY 0 |
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# | 0 0 1 |
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@@ -403,7 +403,7 @@ proc `&=`*(v:var Vector2d,m:Matrix2d) {.inline.}=
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## Applies transformation `m` onto `v` in place.
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## Transforming a vector ignores the translational part
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## of the matrix.
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# | AX AY 0 |
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# | X Y 1 | * | BX BY 0 |
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# | 0 0 1 |
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@@ -412,31 +412,31 @@ proc `&=`*(v:var Vector2d,m:Matrix2d) {.inline.}=
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v.x=newx
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proc tryNormalize*(v:var Vector2d):bool=
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proc tryNormalize*(v:var Vector2d):bool=
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## Modifies `v` to have a length of 1.0, keeping its angle.
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## If `v` has zero length (and thus no angle), it is left unmodified and
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## If `v` has zero length (and thus no angle), it is left unmodified and
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## false is returned, otherwise true is returned.
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let mag=v.len
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if mag==0.0:
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return false
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v.x/=mag
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v.y/=mag
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return true
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proc normalize*(v:var Vector2d) {.inline.}=
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proc normalize*(v:var Vector2d) {.inline.}=
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## Modifies `v` to have a length of 1.0, keeping its angle.
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## If `v` has zero length, an EDivByZero will be raised.
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if not tryNormalize(v):
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raise newException(DivByZeroError,"Cannot normalize zero length vector")
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proc transformNorm*(v:var Vector2d,t:Matrix2d)=
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## Applies a normal direction transformation `t` onto `v` in place.
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## The resulting vector is *not* normalized. Transforming a vector ignores the
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## translational part of the matrix. If the matrix is not invertible
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## The resulting vector is *not* normalized. Transforming a vector ignores the
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## translational part of the matrix. If the matrix is not invertible
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## (determinant=0), an EDivByZero will be raised.
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# transforming a normal is done by transforming
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@@ -469,16 +469,16 @@ proc transformInv*(v:var Vector2d,t:Matrix2d)=
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proc transformNormInv*(v:var Vector2d,t:Matrix2d)=
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## Applies an inverse normal direction transformation `t` onto `v` in place.
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## This is faster than creating an inverse
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## matrix and transformNorm(...) it. Transforming a vector ignores the
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## This is faster than creating an inverse
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## matrix and transformNorm(...) it. Transforming a vector ignores the
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## translational part of the matrix.
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# normal inverse transform is done by transforming
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# by the inverse of the transpose of the inverse of the org. matrix
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# which is equivalent with transforming with the transpose.
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# | | | AX AY 0 |^-1|^T|^-1 | AX BX 0 |
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# | X Y 1 | * | | | BX BY 0 | | | = | X Y 1 | * | AY BY 0 |
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# | | | 0 0 1 | | | | 0 0 1 |
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# | X Y 1 | * | | | BX BY 0 | | | = | X Y 1 | * | AY BY 0 |
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# | | | 0 0 1 | | | | 0 0 1 |
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# This can be heavily reduced to:
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let newx=t.ay*v.y+t.ax*v.x
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v.y=t.by*v.y+t.bx*v.x
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@@ -489,19 +489,19 @@ proc rotate90*(v:var Vector2d) {.inline.}=
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## without using any trigonometrics.
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swap(v.x,v.y)
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v.x= -v.x
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proc rotate180*(v:var Vector2d){.inline.}=
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## Quickly rotates vector `v` 180 degrees counter clockwise,
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## without using any trigonometrics.
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v.x= -v.x
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v.y= -v.y
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proc rotate270*(v:var Vector2d) {.inline.}=
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## Quickly rotates vector `v` 270 degrees counter clockwise,
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## without using any trigonometrics.
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swap(v.x,v.y)
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v.y= -v.y
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proc rotate*(v:var Vector2d,rad:float) =
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## Rotates vector `v` `rad` radians in place.
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let
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@@ -510,18 +510,18 @@ proc rotate*(v:var Vector2d,rad:float) =
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newx=c*v.x-s*v.y
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v.y=c*v.y+s*v.x
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v.x=newx
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proc scale*(v:var Vector2d,fac:float){.inline.}=
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## Scales vector `v` `rad` radians in place.
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v.x*=fac
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v.y*=fac
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proc stretch*(v:var Vector2d,facx,facy:float){.inline.}=
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## Stretches vector `v` `facx` times horizontally,
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## and `facy` times vertically.
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v.x*=facx
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v.y*=facy
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proc mirror*(v:var Vector2d,mirrvec:Vector2d)=
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## Mirrors vector `v` using `mirrvec` as mirror direction.
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let
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@@ -530,20 +530,20 @@ proc mirror*(v:var Vector2d,mirrvec:Vector2d)=
|
||||
nd=1.0/(sqx+sqy) #used to normalize invector
|
||||
xy2=mirrvec.x*mirrvec.y*2.0*nd
|
||||
sqd=nd*(sqx-sqy)
|
||||
|
||||
|
||||
if nd==Inf or nd==NegInf:
|
||||
return #mirroring around a zero vector is arbitrary=>keep as is is fastest
|
||||
|
||||
|
||||
let newx=xy2*v.y+sqd*v.x
|
||||
v.y=v.x*xy2-sqd*v.y
|
||||
v.x=newx
|
||||
|
||||
|
||||
|
||||
|
||||
proc `-` *(v:Vector2d):Vector2d=
|
||||
## Negates a vector
|
||||
result.x= -v.x
|
||||
result.y= -v.y
|
||||
|
||||
|
||||
# declare templated binary operators
|
||||
makeBinOpVector(`+`)
|
||||
makeBinOpVector(`-`)
|
||||
@@ -556,27 +556,27 @@ makeBinOpAssignVector(`/=`)
|
||||
|
||||
|
||||
proc dot*(v1,v2:Vector2d):float=
|
||||
## Computes the dot product of two vectors.
|
||||
## Computes the dot product of two vectors.
|
||||
## Returns 0.0 if the vectors are perpendicular.
|
||||
return v1.x*v2.x+v1.y*v2.y
|
||||
|
||||
|
||||
proc cross*(v1,v2:Vector2d):float=
|
||||
## Computes the cross product of two vectors, also called
|
||||
## the 'perpendicular dot product' in 2d. Returns 0.0 if the vectors
|
||||
## are parallel.
|
||||
return v1.x*v2.y-v1.y*v2.x
|
||||
|
||||
|
||||
proc equals*(v1,v2:Vector2d,tol=1.0e-6):bool=
|
||||
## Checks if two vectors approximately equals with a tolerance.
|
||||
return abs(v2.x-v1.x)<=tol and abs(v2.y-v1.y)<=tol
|
||||
|
||||
|
||||
proc `=~` *(v1,v2:Vector2d):bool=
|
||||
## Checks if two vectors approximately equals with a
|
||||
## Checks if two vectors approximately equals with a
|
||||
## hardcoded tolerance 1e-6
|
||||
equals(v1,v2)
|
||||
|
||||
|
||||
proc angleTo*(v1,v2:Vector2d):float=
|
||||
## Returns the smallest of the two possible angles
|
||||
## Returns the smallest of the two possible angles
|
||||
## between `v1` and `v2` in radians.
|
||||
var
|
||||
nv1=v1
|
||||
@@ -584,7 +584,7 @@ proc angleTo*(v1,v2:Vector2d):float=
|
||||
if not nv1.tryNormalize or not nv2.tryNormalize:
|
||||
return 0.0 # zero length vector has zero angle to any other vector
|
||||
return safeArccos(dot(nv1,nv2))
|
||||
|
||||
|
||||
proc angleCCW*(v1,v2:Vector2d):float=
|
||||
## Returns the counter clockwise plane angle from `v1` to `v2`,
|
||||
## in range 0 - 2*PI
|
||||
@@ -592,7 +592,7 @@ proc angleCCW*(v1,v2:Vector2d):float=
|
||||
if v1.cross(v2)>=0.0:
|
||||
return a
|
||||
return DEG360-a
|
||||
|
||||
|
||||
proc angleCW*(v1,v2:Vector2d):float=
|
||||
## Returns the clockwise plane angle from `v1` to `v2`,
|
||||
## in range 0 - 2*PI
|
||||
@@ -612,32 +612,32 @@ proc turnAngle*(v1,v2:Vector2d):float=
|
||||
proc bisect*(v1,v2:Vector2d):Vector2d {.noInit.}=
|
||||
## Computes the bisector between v1 and v2 as a normalized vector.
|
||||
## If one of the input vectors has zero length, a normalized version
|
||||
## of the other is returned. If both input vectors has zero length,
|
||||
## 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 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
|
||||
|
||||
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
|
||||
# there are actually two bisectors, we select just
|
||||
# one of them (x1,y1 rotated 90 degrees ccw).
|
||||
result.x = -y1
|
||||
result.y = x1
|
||||
@@ -651,13 +651,13 @@ proc bisect*(v1,v2:Vector2d):Vector2d {.noInit.}=
|
||||
proc point2d*(x,y:float):Point2d =
|
||||
result.x=x
|
||||
result.y=y
|
||||
|
||||
|
||||
proc sqrDist*(a,b:Point2d):float=
|
||||
## Computes the squared distance between `a` and `b`
|
||||
let dx=b.x-a.x
|
||||
let dy=b.y-a.y
|
||||
result=dx*dx+dy*dy
|
||||
|
||||
|
||||
proc dist*(a,b:Point2d):float {.inline.}=
|
||||
## Computes the absolute distance between `a` and `b`
|
||||
result=sqrt(sqrDist(a,b))
|
||||
@@ -675,11 +675,11 @@ proc `$` *(p:Point2d):string=
|
||||
result=rtos(p.x)
|
||||
result.add(",")
|
||||
result.add(rtos(p.y))
|
||||
|
||||
|
||||
proc `&`*(p:Point2d,t:Matrix2d):Point2d {.noInit,inline.} =
|
||||
## Concatenates a point `p` with a transform `t`,
|
||||
## resulting in a new, transformed point.
|
||||
|
||||
|
||||
# | AX AY 0 |
|
||||
# | X Y 1 | * | BX BY 0 |
|
||||
# | TX TY 1 |
|
||||
@@ -697,21 +697,21 @@ proc transformInv*(p:var Point2d,t:Matrix2d){.inline.}=
|
||||
## Applies the inverse of transformation `t` onto `p` in place.
|
||||
## If the matrix is not invertable (determinant=0) , EDivByZero will
|
||||
## be raised.
|
||||
|
||||
|
||||
# | AX AY 0 | ^-1
|
||||
# | X Y 1 | * | BX BY 0 |
|
||||
# | TX TY 1 |
|
||||
let d=t.determinant
|
||||
if d==0.0:
|
||||
raise newException(DivByZeroError,"Cannot invert a zero determinant matrix")
|
||||
let
|
||||
let
|
||||
newx= (t.bx*t.ty-t.by*t.tx+p.x*t.by-p.y*t.bx)/d
|
||||
p.y = -(t.ax*t.ty-t.ay*t.tx+p.x*t.ay-p.y*t.ax)/d
|
||||
p.x=newx
|
||||
|
||||
|
||||
|
||||
|
||||
proc `+`*(p:Point2d,v:Vector2d):Point2d {.noInit,inline.} =
|
||||
## Adds a vector `v` to a point `p`, resulting
|
||||
## Adds a vector `v` to a point `p`, resulting
|
||||
## in a new point.
|
||||
result.x=p.x+v.x
|
||||
result.y=p.y+v.y
|
||||
@@ -722,7 +722,7 @@ proc `+=`*(p:var Point2d,v:Vector2d) {.noInit,inline.} =
|
||||
p.y+=v.y
|
||||
|
||||
proc `-`*(p:Point2d,v:Vector2d):Point2d {.noInit,inline.} =
|
||||
## Subtracts a vector `v` from a point `p`, resulting
|
||||
## Subtracts a vector `v` from a point `p`, resulting
|
||||
## in a new point.
|
||||
result.x=p.x-v.x
|
||||
result.y=p.y-v.y
|
||||
@@ -736,13 +736,13 @@ proc `-=`*(p:var Point2d,v:Vector2d) {.noInit,inline.} =
|
||||
## Subtracts a vector `v` from a point `p` in place.
|
||||
p.x-=v.x
|
||||
p.y-=v.y
|
||||
|
||||
|
||||
proc equals(p1,p2:Point2d,tol=1.0e-6):bool {.inline.}=
|
||||
## Checks if two points approximately equals with a tolerance.
|
||||
return abs(p2.x-p1.x)<=tol and abs(p2.y-p1.y)<=tol
|
||||
|
||||
proc `=~`*(p1,p2:Point2d):bool {.inline.}=
|
||||
## Checks if two vectors approximately equals with a
|
||||
## Checks if two vectors approximately equals with a
|
||||
## hardcoded tolerance 1e-6
|
||||
equals(p1,p2)
|
||||
|
||||
@@ -759,7 +759,7 @@ proc rotate*(p:var Point2d,rad:float)=
|
||||
newx=p.x*c-p.y*s
|
||||
p.y=p.y*c+p.x*s
|
||||
p.x=newx
|
||||
|
||||
|
||||
proc rotate*(p:var Point2d,rad:float,org:Point2d)=
|
||||
## Rotates a point in place `rad` radians using `org` as
|
||||
## center of rotation.
|
||||
@@ -769,25 +769,25 @@ proc rotate*(p:var Point2d,rad:float,org:Point2d)=
|
||||
newx=(p.x - org.x) * c - (p.y - org.y) * s + org.x
|
||||
p.y=(p.y - org.y) * c + (p.x - org.x) * s + org.y
|
||||
p.x=newx
|
||||
|
||||
|
||||
proc scale*(p:var Point2d,fac:float) {.inline.}=
|
||||
## Scales a point in place `fac` times with world origo as origin.
|
||||
p.x*=fac
|
||||
p.y*=fac
|
||||
|
||||
|
||||
proc scale*(p:var Point2d,fac:float,org:Point2d){.inline.}=
|
||||
## Scales the point in place `fac` times with `org` as origin.
|
||||
p.x=(p.x - org.x) * fac + org.x
|
||||
p.y=(p.y - org.y) * fac + org.y
|
||||
|
||||
proc stretch*(p:var Point2d,facx,facy:float){.inline.}=
|
||||
## Scales a point in place non uniformly `facx` and `facy` times with
|
||||
## Scales a point in place non uniformly `facx` and `facy` times with
|
||||
## world origo as origin.
|
||||
p.x*=facx
|
||||
p.y*=facy
|
||||
|
||||
proc stretch*(p:var Point2d,facx,facy:float,org:Point2d){.inline.}=
|
||||
## Scales the point in place non uniformly `facx` and `facy` times with
|
||||
## 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.y - org.y) * facy + org.y
|
||||
@@ -814,21 +814,21 @@ proc area*(a,b,c:Point2d):float=
|
||||
return abs(sgnArea(a,b,c))
|
||||
|
||||
proc closestPoint*(p:Point2d,pts:varargs[Point2d]):Point2d=
|
||||
## Returns a point selected from `pts`, that has the closest
|
||||
## Returns a point selected from `pts`, that has the closest
|
||||
## euclidean distance to `p`
|
||||
assert(pts.len>0) # must have at least one point
|
||||
|
||||
var
|
||||
|
||||
var
|
||||
bestidx=0
|
||||
bestdist=p.sqrDist(pts[0])
|
||||
curdist:float
|
||||
|
||||
|
||||
for idx in 1..high(pts):
|
||||
curdist=p.sqrDist(pts[idx])
|
||||
if curdist<bestdist:
|
||||
bestidx=idx
|
||||
bestdist=curdist
|
||||
|
||||
|
||||
result=pts[bestidx]
|
||||
|
||||
|
||||
@@ -843,7 +843,7 @@ proc normAngle*(ang:float):float=
|
||||
return ang
|
||||
|
||||
return ang mod DEG360
|
||||
|
||||
|
||||
proc degToRad*(deg:float):float {.inline.}=
|
||||
## converts `deg` degrees to radians
|
||||
deg / RAD2DEGCONST
|
||||
@@ -852,4 +852,4 @@ proc radToDeg*(rad:float):float {.inline.}=
|
||||
## converts `rad` radians to degrees
|
||||
rad * RAD2DEGCONST
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user