Bernstein basis polynomials: Difference between revisions
Added C
(→{{header|ATS}}: More pedagogical commentary. Also, I modularized the polynomial-printing code, demonstrating more aspects of the type system.) |
(Added C) |
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Line 943:
bern (1.000000, 1.000000, 1.000000) --> bern (1.000000, 1.000000, 1.000000, 1.000000)
bern (1.000000, 2.000000, 6.000000) --> bern (1.000000, 1.666667, 3.333333, 6.000000)</pre>
=={{header|C}}==
{{trans|Wren}}
<syntaxhighlight lang="c">#include <stdio.h>
typedef double dbl;
void tobern2(dbl a0, dbl a1, dbl a2, dbl *b0, dbl *b1, dbl *b2) {
*b0 = a0;
*b1 = a0 + a1 / 2;
*b2 = a0 + a1 + a2;
}
/* uses de Casteljau’s algorithm */
dbl evalbern2(dbl b0, dbl b1, dbl b2, dbl t) {
dbl s = 1.0 - t;
dbl b01 = s * b0 + t * b1;
dbl b12 = s * b1 + t * b2;
return s * b01 + t * b12;
}
void tobern3(dbl a0, dbl a1, dbl a2, dbl a3, dbl *b0, dbl *b1, dbl *b2, dbl *b3) {
*b0 = a0;
*b1 = a0 + a1 / 3;
*b2 = a0 + a1 * 2/3 + a2 / 3;
*b3 = a0 + a1 + a2 + a3;
}
/* uses de Casteljau’s algorithm */
dbl evalbern3(dbl b0, dbl b1, dbl b2, dbl b3, dbl t) {
dbl s = 1 - t;
dbl b01 = s * b0 + t * b1;
dbl b12 = s * b1 + t * b2;
dbl b23 = s * b2 + t * b3;
dbl b012 = s * b01 + t * b12;
dbl b123 = s * b12 + t * b23;
return s * b012 + t * b123;
}
void bern2to3(dbl q0, dbl q1, dbl q2, dbl *c0, dbl *c1, dbl *c2, dbl *c3) {
*c0 = q0;
*c1 = q0 / 3 + q1 * 2/3;
*c2 = q1 * 2/3 + q2 / 3;
*c3 = q2;
}
/* uses Horner's rule */
dbl evalmono2(dbl a0, dbl a1, dbl a2, dbl t) {
return a0 + (t * (a1 + (t * a2)));
}
/* uses Horner's rule */
dbl evalmono3(dbl a0, dbl a1, dbl a2, dbl a3, dbl t) {
return a0 + (t * (a1 + (t * (a2 + (t * a3)))));
}
int main() {
dbl pm0 = 1, pm1 = 0, pm2 = 0, pm3 = 0, pb0, pb1, pb2, pb3, pc0, pc1, pc2, pc3;
dbl qm0 = 1, qm1 = 2, qm2 = 3, qm3 = 0, qb0, qb1, qb2, qb3, qc0, qc1, qc2, qc3;
dbl rm0 = 1, rm1 = 2, rm2 = 3, rm3 = 4, rb0, rb1, rb2, rb3;
dbl x, y, m;
const char *fmt;
printf("Subprogram(1) examples:\n");
tobern2(pm0, pm1, pm2, &pb0, &pb1, &pb2);
tobern2(qm0, qm1, qm2, &qb0, &qb1, &qb2);
fmt = "mono {%g, %g, %g} --> bern {%g, %g, %g}\n";
printf(fmt, pm0, pm1, pm2, pb0, pb1, pb2);
printf(fmt, qm0, qm1, qm2, qb0, qb1, qb2);
printf("\nSubprogram(2) examples:\n");
x = 0.25;
y = evalbern2(pb0, pb1, pb2, x);
m = evalmono2(pm0, pm1, pm2, x);
printf("p(%4.2f) = %g (mono %g)\n", x, y, m);
x = 7.5;
y = evalbern2(pb0, pb1, pb2, x);
m = evalmono2(pm0, pm1, pm2, x);
printf("p(%4.2f) = %g (mono %g)\n", x, y, m);
x = 0.25;
y = evalbern2(qb0, qb1, qb2, x);
m = evalmono2(qm0, qm1, qm2, x);
printf("q(%4.2f) = %g (mono %g)\n", x, y, m);
x = 7.5;
y = evalbern2(qb0, qb1, qb2, x);
m = evalmono2(qm0, qm1, qm2, x);
printf("q(%4.2f) = %g (mono %g)\n", x, y, m);
printf("\nSubprogram(3) examples:\n");
tobern3(pm0, pm1, pm2, pm3, &pb0, &pb1, &pb2, &pb3);
tobern3(qm0, qm1, qm2, qm3, &qb0, &qb1, &qb2, &qb3);
tobern3(rm0, rm1, rm2, rm3, &rb0, &rb1, &rb2, &rb3);
fmt = "mono {%g, %g, %g, %g} --> bern {%0.14g, %0.14g, %0.14g, %0.14g}\n";
printf(fmt, pm0, pm1, pm2, pm3, pb0, pb1, pb2, pb3);
printf(fmt, qm0, qm1, qm2, qm3, qb0, qb1, qb2, qb3);
printf(fmt, rm0, rm1, rm2, rm3, rb0, rb1, rb2, rb3);
printf("\nSubprogram(4) examples:\n");
x = 0.25;
y = evalbern3(pb0, pb1, pb2, pb3, x);
m = evalmono3(pm0, pm1, pm2, pm3, x);
printf("p(%4.2f) = %g (mono %g)\n", x, y, m);
x = 7.5;
y = evalbern3(pb0, pb1, pb2, pb3, x);
m = evalmono3(pm0, pm1, pm2, pm3, x);
printf("p(%4.2f) = %g (mono %g)\n", x, y, m);
x = 0.25;
y = evalbern3(qb0, qb1, qb2, qb3, x);
m = evalmono3(qm0, qm1, qm2, qm3, x);
printf("q(%4.2f) = %g (mono %g)\n", x, y, m);
x = 7.5;
y = evalbern3(qb0, qb1, qb2, qb3, x);
m = evalmono3(qm0, qm1, qm2, qm3, x);
printf("q(%4.2f) = %g (mono %g)\n", x, y, m);
x = 0.25;
y = evalbern3(rb0, rb1, rb2, rb3, x);
m = evalmono3(rm0, rm1, rm2, rm3, x);
printf("r(%4.2f) = %g (mono %g)\n", x, y, m);
x = 7.5;
y = evalbern3(rb0, rb1, rb2, rb3, x);
m = evalmono3(rm0, rm1, rm2, rm3, x);
printf("r(%4.2f) = %g (mono %g)\n", x, y, m);
printf("\nSubprogram(5) examples:\n");
tobern2(pm0, pm1, pm2, &pb0, &pb1, &pb2);
tobern2(qm0, qm1, qm2, &qb0, &qb1, &qb2);
bern2to3(pb0, pb1, pb2, &pc0, &pc1, &pc2, &pc3);
bern2to3(qb0, qb1, qb2, &qc0, &qc1, &qc2, &qc3);
fmt = "mono {%g, %g, %g} --> bern {%0.14g, %0.14g, %0.14g, %0.14g}\n";
printf(fmt, pb0, pb1, pb2, pc0, pc1, pc2, pc3);
printf(fmt, qb0, qb1, qb2, qc0, qc1, qc2, qc3);
return 0;
}</syntaxhighlight>
{{out}}
<pre>
Subprogram(1) examples:
mono {1, 0, 0} --> bern {1, 1, 1}
mono {1, 2, 3} --> bern {1, 2, 6}
Subprogram(2) examples:
p(0.25) = 1 (mono 1)
p(7.50) = 1 (mono 1)
q(0.25) = 1.6875 (mono 1.6875)
q(7.50) = 184.75 (mono 184.75)
Subprogram(3) examples:
mono {1, 0, 0, 0} --> bern {1, 1, 1, 1}
mono {1, 2, 3, 0} --> bern {1, 1.6666666666667, 3.3333333333333, 6}
mono {1, 2, 3, 4} --> bern {1, 1.6666666666667, 3.3333333333333, 10}
Subprogram(4) examples:
p(0.25) = 1 (mono 1)
p(7.50) = 1 (mono 1)
q(0.25) = 1.6875 (mono 1.6875)
q(7.50) = 184.75 (mono 184.75)
r(0.25) = 1.75 (mono 1.75)
r(7.50) = 1872.25 (mono 1872.25)
Subprogram(5) examples:
mono {1, 1, 1} --> bern {1, 1, 1, 1}
mono {1, 2, 6} --> bern {1, 1.6666666666667, 3.3333333333333, 6}
</pre>
=={{header|FreeBASIC}}==
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