A method for mapping during a medical procedure a surface that contains a volume in 3D space, the surface comprising an internal surface of a heart or a temperature distribution map of an internal surface of the heart measured around a distal tip of a catheter, the method comprising: acquiring from tracking of the catheter, or from the geometry of the distal tip of the catheter, a set of 3D vertices representing the surface; producing a 3D mesh from the 3D vertices; defining a first plane that cuts the mesh and a second plane , parallel to the first plane , that is external to the mesh, the second plane having a point B and a line through point B, the line being orthogonal to the first and second planes, thereby partitioning the 3D vertices into a first set of the vertices that are not between the first and second planes and a second set of the vertices that are located between the first and the second planes ; projecting the vertices in the first set onto the first plane orthogonally so as to generate first projected points in the first plane ; projecting the vertices in the second set onto the first plane while translating the vertices in the second set in respective directions parallel to the second plane by respective translations, wherein for each vertex in the second set of vertices the translation is directly proportional to the distance of the vertex from the first plane and to the distance, measured parallel to the planes, of the vertex from point wherein the direction of the translation corresponds to the direction of the original vertex from the line through point B, thereby generating second projected points in the first plane ; and displaying the first and second projected points of the first plane together as a two-dimensional representation of the surface of the internal surface of the heart or the temperature distribution map of the internal surface of the heart measured around the distal tip of the catheter on a screen , with the line through point B being orthogonal to the screen. acquiring from tracking of the catheter, or from the geometry of the distal tip of the catheter, a set of 3D vertices representing the surface; producing a 3D mesh from the 3D vertices; defining a first plane that cuts the mesh and a second plane , parallel to the first plane , that is external to the mesh, the second plane having a point B and a line through point B, the line being orthogonal to the first and second planes, thereby partitioning the 3D vertices into a first set of the vertices that are not between the first and second planes and a second set of the vertices that are located between the first and the second planes ; projecting the vertices in the first set onto the first plane orthogonally so as to generate first projected points in the first plane ; projecting the vertices in the second set onto the first plane while translating the vertices in the second set in respective directions parallel to the second plane by respective translations, wherein for each vertex in the second set of vertices the translation is directly proportional to the distance of the vertex from the first plane and to the distance, measured parallel to the planes, of the vertex from point wherein the direction of the translation corresponds to the direction of the original vertex from the line through point B, thereby generating second projected points in the first plane ; and displaying the first and second projected points of the first plane together as a two-dimensional representation of the surface of the internal surface of the heart or the temperature distribution map of the internal surface of the heart measured around the distal tip of the catheter on a screen , with the line through point B being orthogonal to the screen. <EOS>