4 5 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]

MS.matToSys(mat) : convert a matrix to a system. Note: matrix has to be a mx1 matrix

mat MS.matToSys ret 0 1 1 sys : j 1 mat rows range ret j el mat j el : for ret 3 1 line :

MS.matToSys_EX1 : A simple example of matToSys

wwooo haaa man 34 WHOa 3 45 sin 5 ! 2 2 mat 3 1 mat MS.matToSys wwooo haaa man 34 WHOa 3 0.8509035245 120 2 2 mat 3 1 sys

GF.approxEllipse: Approximate Ellipse as a series of vectors inp: [ "horzRad": num/"NULL" radius of major axis - if "NULL", a will be interpolated by aCord-Center.x "vertRad": num/"NULL" radius of minor axis - if "NULL", b will be interpolated by bCord-Center.y "horzCoord": x co-ordinate of horizontal axis "vertCoord": y co-ordinate of vertical axis "center": 1x2/2x2 co-ordinates of center "retType": "sys"/"mat" - type of data to return "begAngle": numDegrees - start angle of ellipse "endAngle": numDegrees - end angle of ellipse "numPoints": num - number of points to represent ellipse with ]

inp GF.approxEllipse k 1 inp rows range holder inp k 2 el : inp k 1 el :holder concat str2num 2 1 line for find_a_and_b_if_necessary horzRad IsString 1 ≡ horzRad NULL ≡ a horzCoord center 1 1 el - : unknown_horzCoord_entry error if a horzRad : if vertRad IsString 1 ≡ vertRad NULL ≡ b vertCoord center 1 2 el - : unknown_vertCoord_entry error if b vertRad : if develope_angles θ endAng begAng - numPoints / eval : thetas numPoints 1 matrix : k 1 numPoints 1 + range thetas k el k 1 - ( θ * begAng + : for center rows 1 ≡ center center center stack : center rows 2 ≡ centers fine unknown_center_point_in_approxCircle error if if initiazlie_return_matrix_and_return retMat numPoints 1 matrix : k 1 numPoints range rad1 a b * b thetas k el cos * ( 2 ^ a thetas k el sin * ( 2 ^ + sqrt / eval : rad2 a b * b thetas k 1 + el cos * ( 2 ^ a thetas k 1 + el sin * ( 2 ^ + sqrt / eval : retMat k el rad1 thetas k el cos * rad1 thetas k el sin * rad2 thetas k 1 + el cos * rad2 thetas k 1 + el sin * 2 2 mat ( center + eval : 3 1 line for retType mat ≡ ret retMat : retType sys ≡ ret retMat MS.matToSys : unknown_return_type_in_approxCircle error if if ret 14 1 line :

GF.approxCircle_EX_1: Unit Circle Example

 horzRad 1 vertRad 1 horzCoord NULL vertCoord NULL center 0 0 1 2 mat numPoints 40 retType sys begAng 0 deg * endAng 360 deg * 9 2 mat GF.approxEllipse

GF.approxEllipse_EX_2: Define ellipse by co-ordinates

 horzRad NULL vertRad NULL horzCoord 10 vertCoord 9 center 5 7 1 2 mat numPoints 40 retType sys begAng 0 deg * endAng 360 deg * 9 2 mat GF.approxEllipse

GF.approxCircle_EX_3: draw a portion of ellipse

 horzRad NULL vertRad NULL horzCoord 1 vertCoord 3 center 5 - 1 1 2 mat numPoints 20 retType sys begAng 90 deg * endAng 270 deg * 9 2 mat GF.approxEllipse

GF.approxCircle_EX_4: draw a portion of ellipse

 horzRad NULL vertRad NULL horzCoord 1 vertCoord 3 center 5 - 1 - 1 2 mat numPoints 20 retType sys begAng 90 deg * endAng 270 deg * 9 2 mat GF.approxEllipse