Compare the following two parameterizations of a circle pt

Compare the following two parameterizations of a circle: p(t) = [cos(t) sin(t)], 0 lessthanorequalto t lessthanorequalto 1 p(t) = [1-t^2/1+t^2 2t/1+t^2], -infinity lessthanorequalto t lessthanorequalto infinity Verify that both parameterizations represent the circle Evaluate the \"speed\" for each parameterization. Which parameterization would you use if you need to generate points at regular arc-length intervals (for example, to draw the curve on the screen)?

Solution

#include #include #define MAX 20 void maxheapify(int *, int, int); int* buildmaxheap(int *, int); void main() { int i, t, n; int *a = calloc(MAX, sizeof(int)); int *m = calloc(MAX, sizeof(int)); printf(\"Enter no of elements in the array\ \"); scanf(\"%d\", &n); printf(\"Enter the array\ \"); for (i = 0; i < n; i++) { scanf(\"%d\", &a[i]); } m = buildmaxheap(a, n); printf(\"The heap is\ \"); for (t = 0; t < n; t++) { printf(\"%d\ \", m[t]); } } int* buildmaxheap(int a[], int n) { int heapsize = n; int j; for (j = n/2; j >= 0; j--) { maxheapify(a, j, heapsize); } return a; } void maxheapify(int a[], int i, int heapsize) { int temp, largest, left, right, k; left = (2*i+1); right = ((2*i)+2); if (left >= heapsize) return; else { if (left < (heapsize) && a[left] > a[i]) largest = left; else largest = i; if (right < (heapsize) && a[right] > a[largest]) largest = right; if (largest != i) { temp = a[i]; a[i] = a[largest]; a[largest] = temp; maxheapify(a, largest, heapsize); } } }