C++ How to scale a shape and create an if function to not print if too big after scale? - c++

Question

given a shapes orignal centroid + vertices .. i.e. if its a triangle, i know all three vertices coords. How could i then create a scaling function with a scaling factor as a parameter as below.. however my current code is with error and the result are huge shapes, much more than what im scaling by (only want scale factor of 2).
void Shape::scale(double factor)
{
int x, y, xx, xy;
int disx, disy;
for (itr = vertices.begin(); itr != vertices.end(); ++itr) {
//translate obj to origin (0,0)
x = itr->getX() - centroid.getX();
y = itr->getY() - centroid.getY();
//finds distance between centroid and vertex
disx = x + itr->getX();
disy = y + itr->getY();
xx = disx * factor;
xy = disy * factor;
//translate obj back
xx = xx + centroid.getX();
xy = xy + centroid.getY();
//set new coord
itr->setX(xx);
itr->setY(xy);
}
}
I know of using iterations to run through the vertices, my main point of confusion is how can i do the maths between the factor to scale my shapes size?
this is how i declare and itialise a vertex
// could i possible do (scale*x,scale*y)? or would that be problematic..
vertices.push_back(Vertex(x, y));
Also.. the grid is i.e. 100x100. if a scaled shape was to be too big to fit into that grid, i want an exit from the scale function so that the shape wont be enlarged, how can this be done effectively? so far i have a for look but that just loops on vertices, so it will only stop those that would be outside the grid, instead of cancelling the entire shape which would be ideal
if my question is too broad, please ask and i shall edit further to standard

Answer 1

First thing you need to do is find the center of mass of your set of points. That is the arithmetic mean of the coordinates of your points. Then, for each point calculate the line between the center of mass and that point. Now the only thing left is to put the point on that line, but in factor * current_distance away, where current_distance is the distance from the mass center to the given point before rescaling.
void Shape::scale(double factor)
{
Vertex mass_center = Vertex(0., 0.);
for(int i = 0; i < vertices.size(); i++)
{
mass_center.x += vertices[i].x;
mass_center.y += vertices[i].y;
}
mass_center.x /= vertices.size();
mass_center.y /= vertices.size();
for(int i = 0; i < vertices.size(); i++)
{
//this is a vector that leads from mass center to current vertex
Vertex vec = Vertex(vertices[i].x - mass_center.x, vertices[i].y - mass_center.y);
vertices[i].x = mass_center.x + factor * vec.x;
vertices[i].y = mass_center.y + factor * vec.y;
}
}

Answer 2

If you already know the centroid of a shape and the vertexes are the distance from that point then scaling in rectangular coordinates is just multiplying the x and y components of each vertex by the appropriate scaling factor (with a negative value flipping the shape around the axis.
void Shape::scale(double x_factor, double y_factor){
for(auto i=0; i < verticies.size();++i){
verticies[i].x *= x_scale;
verticies[i].y *= y_scale;
}
}
You could then just overload this function with one that takes a single parameter and calls this function with the same value for x and y.
void Shape::scale(double factor){
Shape::scale(factor, factor);
}
If you're vertex values are not centered at the origin then you will also have to multiply those values by your scaling factor.