How can I transform the sprites like that?
This is an interesting problem, so I've taken some time to implement it

First, you need to reflect how to achieve the functionality with the SFML 2 API. I operate on two sf::Image objects and use a texture mapping transform. That is, every pixel of the destination image is mapped to one of the source image. Actually, we are not mapping a rectangle to a circle sector piece, but performing the inverse transform. If you are not familiar with std::function, take a look at the Boost.Function documentation.
#include <SFML/Graphics/Image.hpp>
#include <functional>
// Function that maps every pixel of dest to source, according to the transform
// transform: Takes pixel coordinates, returns texture coordinate vector with components in [0.f, 1.f]
void ApplyTransform(const sf::Image& source, sf::Image& dest, std::function<sf::Vector2f(unsigned int, unsigned int)> transform)
{
for (unsigned int x = 0; x < dest.GetWidth(); ++x)
for (unsigned int y = 0; y < dest.GetHeight(); ++y)
{
sf::Vector2f texCoords = transform(x, y);
// Invalid texture coordinates lead to transparent pixels
sf::Color color(0, 0, 0, 0);
if (texCoords != sf::Vector2f(-1.f, -1.f))
{
color = source.GetPixel(
static_cast<unsigned int>(source.GetWidth() * texCoords.x),
static_cast<unsigned int>(source.GetHeight() * texCoords.y));
}
dest.SetPixel(x, y, color);
}
}
Now we can pass any callable object as third argument. The core functionality is implemented in the following functor. Additional to SFML, I use polar vectors from Thor because I want to avoid raw trigonometry.
#include <Thor/Vectors/PolarVector.hpp>
// Functor to transform every point in a circle sector piece to a square with width 1
struct CircleSectorPiece
{
// center: Center position of the circle
// r1: Small radius, > 0
// r2: Big radius, > r1
// phi1: Begin angle, in [-180, 180[
// phi2: End angle, in ]phi1, 180]
CircleSectorPiece(sf::Vector2f center, float r1, float r2, float phi1, float phi2)
: center(center)
, r1(r1)
, r2(r2)
, phi1(phi1)
, phi2(phi2)
{
}
sf::Vector2f operator() (unsigned int x, unsigned int y)
{
const sf::Vector2f pixelCoords(sf::Vector2i(x, y));
// Transform difference between current pixel and circle center to polar coordinates
const thor::PolarVector2f vec = pixelCoords - center;
// The actual transform, if point is inside the circle sector piece
if (vec.r > r1 && vec.r < r2 && vec.phi > phi1 && vec.phi < phi2)
{
return sf::Vector2f(
(vec.phi - phi1) / (phi2 - phi1),
1.f - (vec.r - r1) / (r2 - r1));
}
// Point is outside, return invalid texture coordinate
else
{
return sf::Vector2f(-1.f, -1.f);
}
};
sf::Vector2f center;
float r1;
float r2;
float phi1;
float phi2;
};
As you see, the code performing the actual transform is very short. The rest is either boilerplate code (functor) or interop with SFML. A use case might look like this:
sf::Image source, dest;
source.LoadFromFile("image.jpg");
dest.Create(500, 500);
ApplyTransform(source, dest, CircleSectorPiece(sf::Vector2f(200.f, 200.f), 50.f, 300.f, -150.f, -30.f));
It's currently not possible (or at least not easy).
As you see, it is

But out of interest: Does the new API allow such circular transforms? Or would one approximate it with multiple trapezes?