OpenSSL/EC POINT new
An EC_POINT represents a point on a curve. A new point is constructed by calling the function EC_POINT_new and providing the group object that the point relates to.
EC_POINT_free frees the memory associated with the EC_POINT.
EC_POINT_clear_free destroys any sensitive data held within the EC_POINT and then frees its memory.
EC_POINT_copy copies the point src into dst. Both src and dst must use the same EC_METHOD.
EC_POINT_dup creates a new EC_POINT object and copies the content from src to the newly created EC_POINT object.
EC_POINT_method_of obtains the EC_METHOD associated with point.
A valid point on a curve is the special point at infinity. A point is set to be at infinity by calling EC_POINT_set_to_infinity.
The affine co-ordinates for a point describe a point in terms of its x and y position. The functions EC_POINT_set_affine_coordinates_GFp and EC_POINT_set_affine_coordinates_GF2m set the x and y co-ordinates for the point p defined over the curve given in group.
As well as the affine co-ordinates, a point can alternatively be described in terms of its Jacobian projective co-ordinates (for Fp curves only). Jacobian projective co-ordinates are expressed as three values x, y and z. Working in this co-ordinate system provides more efficient point multiplication operations. A mapping exists between Jacobian projective co-ordinates and affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian projective to affine co-ordinates is simple. The co-ordinate (x, y) is mapped to (x, y, 1). To set or get the projective co-ordinates use EC_POINT_set_Jprojective_coordinates_GFp and EC_POINT_get_Jprojective_coordinates_GFp respectively.
Points can also be described in terms of their compressed co-ordinates. For a point (x, y), for any given value for x such that the point is on the curve there will only ever be two possible values for y. Therefore a point can be set using the EC_POINT_set_compressed_coordinates_GFp and EC_POINT_set_compressed_coordinates_GF2m functions where x is the x co-ordinate and y_bit is a value 0 or 1 to identify which of the two possible values for y should be used.
In addition EC_POINTs can be converted to and from various external representations. Supported representations are octet strings, BIGNUMs and hexadecimal. The format of the external representation is described by the point_conversion_form. See EC_GROUP_copy for a description of point_conversion_form. Octet strings are stored in a buffer along with an associated buffer length. A point held in a BIGNUM is calculated by converting the point to an octet string and then converting that octet string into a BIGNUM integer. Points in hexadecimal format are stored in a NULL terminated character string where each character is one of the printable values 0-9 or A-F (or a-f).
Return Values 
EC_POINT_new and EC_POINT_dup return the newly allocated EC_POINT or NULL on error.
The following functions return 1 on success or 0 on error: EC_POINT_copy, EC_POINT_set_to_infinity, EC_POINT_set_Jprojective_coordinates_GFp, EC_POINT_get_Jprojective_coordinates_GFp, EC_POINT_set_affine_coordinates_GFp, EC_POINT_get_affine_coordinates_GFp, EC_POINT_set_compressed_coordinates_GFp, EC_POINT_set_affine_coordinates_GF2m, EC_POINT_get_affine_coordinates_GF2m, EC_POINT_set_compressed_coordinates_GF2m and EC_POINT_oct2point.
EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT.
EC_POINT_point2oct returns the length of the required buffer, or 0 on error.
EC_POINT_point2bn returns the pointer to the BIGNUM supplied, or NULL on error.
EC_POINT_bn2point returns the pointer to the EC_POINT supplied, or NULL on error.
EC_POINT_point2hex returns a pointer to the hex string, or NULL on error.
EC_POINT_hex2point returns the pointer to the EC_POINT supplied, or NULL on error.
The functions EC_POINT_point2oct, EC_POINT_oct2point, EC_POINT_point2bn, EC_POINT_bn2point, EC_POINT_point2hex and EC_POINT_hex2point convert from and to EC_POINTs for the formats: octet string, BIGNUM and hexadecimal respectively.
The function EC_POINT_point2oct must be supplied with a buffer long enough to store the octet string. The return value provides the number of octets stored. Calling the function with a NULL buffer will not perform the conversion but will still return the required buffer length.
The function EC_POINT_point2hex will allocate sufficient memory to store the hexadecimal string. It is the caller's responsibility to free this memory with a subsequent call to OPENSSL_free().