Check whether the polygon is convex - c

Question

I need to check whether the polygon is convex
I know that there were questions here about it, but I need to check the code, whether it is right
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int check_figure(float* x_points[], float* y_points[]);
int main(void) {
int n;
scanf("%i", &n);
int i = 0;
float **x_points = NULL, **y_points = NULL;
x_points = (float**) malloc(sizeof(float*) * (n + 1));
if (x_points == NULL) {
return 0;
}
y_points = (float**) malloc(sizeof(float*) * (n + 1));
if (y_points == NULL) {
return 0;
}
for (i = 0; i < n; i++) {
x_points[i] = (float*) malloc((n + 1) * sizeof(float));
scanf("%f", x_points[i]);
y_points[i] = (float*) malloc((n + 1) * sizeof(float));
scanf("%f", y_points[i]);
}
for (i = 0; i < n - 1; i++) {
if ((x_points[i] == NULL) || (y_points[i] == NULL)) {
return 0;
}
}
x_points[n] = NULL;
y_points[n] = NULL;
int convex = check_figure(x_points, y_points);
if (convex == 1) {
printf("%s", "true");
} else {
printf("%s", "false");
}
free(x_points);
free(y_points);
//free(convex);
return 0;
}
int check_figure(float *x_points[], float *y_points[]) {
float first = 0, booll = 1, sign = 0, result = 0;
int i = 0;
//int *convex = (int*)malloc(sizeof(int));
int convex;
while (1) {
if (x_points[i] != NULL) {
i++;
} else {
break;
}
}
first = *x_points[i - 1] * *y_points[0] - *y_points[i - 1] * *x_points[0];
sign = first / fabsf(first);
int k;
for (k = 0; k < i - 2; k++) {
result = *x_points[k] * *y_points[k + 1] - *x_points[k + 1] * *y_points[k];
booll = booll * sign * result / fabsf(result);
if (booll < 0) {
convex = 0;
return convex;
} else {
convex = 1;
return convex;
}
}
}
there is a sample, for example I input 4 and then I input 0,2; 2,-2; 0,0; -2,-2; and it returns me true, but the polygon is not convex...I really can't get it

Answer 1

A polygon is convex if all of its angles are acute, or 180 degrees (well, then it's not an angle, but depending what your doing, sometimes they happen.) So, just make sure all the angles are acute or 180 degrees.
On 2 dimensions this is not that hard, you just make sure your polygons are always wound the same way, then to test an angle between segments ab and bc, you create another vector by rotating vec2(a - b) 90 degrees towards the middle of the polygon (always the same rotation, because it's always wound the same way. A 90 degree rotation here can be accomplished by flipping the x and y values, and then negating one of the values, based on which way you are rotating.) Then, if the dot product of that rotated vector and the the vector of vec2(c-b) is positive, it is acute, if it is negative, it is obtuse, and if it is 0 it is a straight line. In three dimensions it is also not that hard, but you have to rotate along the same plane as the original angle.
Looking at your code I just have no idea how that is suppose to determine whether or not an angle is acute. At some point you need an angle, or a sine of an angle, or a cosine of an angle (obtained in this method via a dot product), or something somehow related to an angle. There are more direct ways to do this also, this is just a relatively performant one.