Method for manufacturing a product, comprising: - a determination as to whether points in a set of points (11, 30) of a portion of a finite space are inside or outside an object (14, 6), the portion of the finite space comprising said object, said object corresponding to the product to be manufactured or to a part or layer or slice of the product to be manufactured, and - a manufacture of the product from the determination as to whether each point among the set of points is inside or outside the object, a point determined as being inside the object corresponding to a point that must be in a material of the product to be manufactured; said object being broken down into elementary surfaces, a combination of the elementary surfaces forming said object, and in that, for each point (11, 30) among the set of points for which it is sought to determine whether they are inside or outside the object, the method comprises: - a determination of at least one line passing through this point (11, 30) with which a counter dedicated solely to this point is associated, and - an iteration, on each of the elementary surfaces, of the following operations: • a search for an intersection between the elementary surface and the line passing through the point (11, 30), ∘ a modification of the counter if the intersection exists, and - a determination as to whether the point is inside or outside the object according to the value of the counter dedicated solely to the point (11, 30) each of the previous steps being implemented by at least one computer, a central or computing unit, an analogue electronic circuit, a digital electronic circuit, a microprocessor, and/or software means. - a determination as to whether points in a set of points (11, 30) of a portion of a finite space are inside or outside an object (14, 6), the portion of the finite space comprising said object, said object corresponding to the product to be manufactured or to a part or layer or slice of the product to be manufactured, and - a manufacture of the product from the determination as to whether each point among the set of points is inside or outside the object, a point determined as being inside the object corresponding to a point that must be in a material of the product to be manufactured; said object being broken down into elementary surfaces, a combination of the elementary surfaces forming said object, and in that, for each point (11, 30) among the set of points for which it is sought to determine whether they are inside or outside the object, the method comprises: - a determination of at least one line passing through this point (11, 30) with which a counter dedicated solely to this point is associated, and - an iteration, on each of the elementary surfaces, of the following operations: • a search for an intersection between the elementary surface and the line passing through the point (11, 30), ∘ a modification of the counter if the intersection exists, and - a determination as to whether the point is inside or outside the object according to the value of the counter dedicated solely to the point (11, 30) each of the previous steps being implemented by at least one computer, a central or computing unit, an analogue electronic circuit, a digital electronic circuit, a microprocessor, and/or software means. said object being broken down into elementary surfaces, a combination of the elementary surfaces forming said object, and in that, for each point (11, 30) among the set of points for which it is sought to determine whether they are inside or outside the object, the method comprises: - a determination of at least one line passing through this point (11, 30) with which a counter dedicated solely to this point is associated, and - an iteration, on each of the elementary surfaces, of the following operations: • a search for an intersection between the elementary surface and the line passing through the point (11, 30), ∘ a modification of the counter if the intersection exists, and - a determination as to whether the point is inside or outside the object according to the value of the counter dedicated solely to the point (11, 30) - a determination of at least one line passing through this point (11, 30) with which a counter dedicated solely to this point is associated, and - an iteration, on each of the elementary surfaces, of the following operations: • a search for an intersection between the elementary surface and the line passing through the point (11, 30), ∘ a modification of the counter if the intersection exists, and • a search for an intersection between the elementary surface and the line passing through the point (11, 30), ∘ a modification of the counter if the intersection exists, and ∘ a modification of the counter if the intersection exists, and - a determination as to whether the point is inside or outside the object according to the value of the counter dedicated solely to the point (11, 30) each of the previous steps being implemented by at least one computer, a central or computing unit, an analogue electronic circuit, a digital electronic circuit, a microprocessor, and/or software means.