alg036.txt

Numerical Anaysis 8th Edition Burden and Faires (Maple Source)

> restart;
> # BEZIER CURVE ALGORITHM 3.6
> #
> # To construct the cubic Bezier curves C0, ..., Cn-1 in
> # parameter form, where Ci is represented by
> #
> # (xi(t),yi(t)) = ( a0(i) + a1(i)*t + a2(i)*t^2 + a3(i)*t^3,
> #                   b0(i) + b1(i)*t + b2(i)*t^2 + b3(i)*t^3)
> #
> # for 0 <= t <= 1 as determined by the left endpoint (x(i),y(i)),
> # left guidepoint (x+(i),y+(i)), right endpoint (x(i+1),y(i+1)) and
> # right guidepoint (x-(i+1),y-(i+1)) for each i = 0, 1, ... , n-1;
> #
> # INPUT  n, ( (x(i),y(i)), i = 0,...,n ),
> #           ( (x+(i),y+(i)), i = 0,...,n-1 ),
> #           ( (x-(i),y-(i)), i = 1,...,n ).
> #
> # OUTPUT coefficients ( a0(i), a1(i), a2(i), a3(i),
> #                       b0(i), b1(i), b2(i), b3(i), i = 0, ... , n-1 ).
> alg036 := proc() local OK, FLAG, N, X, Y, XPL, YPL, I, XMI, YMI, A, NAME, INP, OUP, A0, B0, A1, B1, A2, B2, A3, B3;
> printf(`This is the Bezier Curve Algorithm.\n`);
> OK := FALSE;
> while OK = FALSE do
> printf(`Choice of input method:\n`);
> printf(`1. Input entry by entry from keyboard\n`);
> printf(`2. Input data from a text file\n`);
> printf(`Choose 1 or 2 please\n`);
> FLAG := scanf(`%d`)[1];
> if FLAG = 1 or FLAG = 2 then
> OK := TRUE;
> fi;
> od;
> if FLAG = 1 then
> OK := FALSE;
> while OK = FALSE do
> printf(`Input n\n`);
> N := scanf(`%d`)[1];
> if N > 0 then
> OK := TRUE;
> printf(`Input X[0],Y[0],X+[0],Y+[0]\n`);
> printf(`separated by a space\n`);
> X[0] := scanf(`%f`)[1];
> Y[0] := scanf(`%f`)[1];
> XPL[0] := scanf(`%f`)[1];
> YPL[0] := scanf(`%f`)[1];
> for I from 1 to N-1 do
> printf(`Input X(%d),Y(%d)\n`, I, I);
> printf(`separated by space\n`);
> X[I] := scanf(`%f`)[1];
> Y[I] := scanf(`%f`)[1];
> printf(`Input X-(%d),Y-(%d)\n`, I, I);
> printf(`separated by space\n`);
> XMI[I-1] := scanf(`%f`)[1];
> YMI[I-1] := scanf(`%f`)[1];
> printf(`Input X+(%d),Y+(%d)\n`, I, I);
> printf(`separated by space\n`);
> XPL[I] := scanf(`%f`)[1];
> YPL[I] := scanf(`%f`)[1];
> od;
> printf(`Input X[n],Y[n],X-[n],Y-[n]\n`);
> printf(`separated by a space\n`);
> X[N] := scanf(`%f`)[1];
> Y[N] := scanf(`%f`)[1];
> XMI[N-1] := scanf(`%f`)[1];
> YMI[N-1] := scanf(`%f`)[1];
> else
> printf(`Number must be a positive integer\n`);
> fi;
> od;
> fi;
> if FLAG = 2 then
> printf(`Has a text file been created with the data as follows ?\n\n`);
> printf(`X[0]    Y[0]    X+[0]    Y+[0]\n`);
> printf(`X[1]    Y[1]    X-[1]    Y-[1]    X+[1]    Y+[1]\n`);
> printf(`...\n`);
> printf(`X[n-1]  Y[n-1]  X-[n-1]  Y-[n-1]  X+[n-1]  Y+[n-1]\n`);
> printf(`X[n]    Y[n]    X-[n]    Y-[n]\n\n`);
> printf(`Enter Y or N\n`);
> A := scanf(`\n%c`)[1];
> if A = "Y" or A = "y" then
> printf(`Input the file name in the form - `);
> printf(`drive:\\name.ext\n`);
> printf(`For example:   A:\\DATA.DTA\n`);
> NAME := scanf(`%s`)[1];
> INP := fopen(NAME,READ,TEXT);
> OK := FALSE;
> while OK = FALSE do
> printf(`Input n\n`);
> N := scanf(`\n%d`)[1];
> if N > 0 then
> OK := TRUE;
> X[0] := fscanf(INP, `%f`)[1];
> Y[0] := fscanf(INP, `%f`)[1];
> XPL[0] := fscanf(INP, `%f`)[1];
> YPL[0] := fscanf(INP, `%f`)[1];
> for I from 1 to N-1 do
> X[I] := fscanf(INP, `%f`)[1];
> Y[I] := fscanf(INP, `%f`)[1];
> XMI[I-1] := fscanf(INP, `%f`)[1];
> YMI[I-1] := fscanf(INP, `%f`)[1];
> XPL[I] := fscanf(INP, `%f`)[1];
> YPL[I] := fscanf(INP, `%f`)[1];
> od;
> X[N] := fscanf(INP, `%f`)[1];
> Y[N] := fscanf(INP, `%f`)[1];
> XMI[N-1] := fscanf(INP, `%f`)[1];
> YMI[N-1] := fscanf(INP, `%f`)[1];
> fclose(INP);
> else
> printf(`Number must be a positive integer\n`);
> fi;
> od;
> else
> printf(`Please create the input file as indicated.\n`);
> printf(`The program will end so the input file can `);
> printf(`be created.\n`);
> OK := FALSE;
> fi;
> fi;
> if OK = TRUE then
> printf(`Select output destination\n`);
> printf(`1. Screen\n`);
> printf(`2. Text file\n`);
> printf(`Enter 1 or 2\n`);
> FLAG := scanf(`%d`)[1];
> if FLAG = 2 then
> printf(`Input the file name in the form - drive:\\name.ext\n`);
> printf(`For example:   A:\\OUTPUT.DTA\n`);
> NAME := scanf(`%s`)[1];
> OUP := fopen(NAME,WRITE,TEXT);
> else
> OUP := default;
> fi;
> fprintf(OUP, `BEZIER CURVE ALGORITHM\n\n`);
> fprintf(OUP, `          A0          A1          A2          A3`);
> fprintf(OUP,`  on the first line\n`);
> fprintf(OUP, `          B0          B1          B2          B3`);
> fprintf(OUP,`  on the second line\n`);
> # Step 1
> for I from 0 to N-1 do
> # Step 2
> A0[I] := X[I];
> B0[I] := Y[I];
> A1[I] := 3*(XPL[I] - X[I]);
> B1[I] := 3*(YPL[I] - Y[I]);
> A2[I] := 3*(X[I]+XMI[I]-2*XPL[I]);
> B2[I] := 3*(Y[I]+YMI[I]-2*YPL[I]);
> A3[I] := X[I+1]-X[I]+3*XPL[I]-3*XMI[I];
> B3[I] := Y[I+1]-Y[I]+3*YPL[I]-3*YMI[I];
> # Step 3
> fprintf(OUP,` %11.6f %11.6f %11.6f %11.6f\n`, A0[I], A1[I], A2[I], A3[I]);
> fprintf(OUP,` %11.6f %11.6f %11.6f %11.6f\n`, B0[I], B1[I], B2[I], B3[I]);
> fprintf(OUP, `\n`);
> od;
> if OUP <> default then
> fclose(OUP);
> printf(`Output file %s created successfully`,NAME);
> fi;
> fi;
> # Step 4
> RETURN(0);
> end;
> alg036();