A method for encoding an organized point cloud representing a scene using an encoder including a processor in communication with a memory, wherein each point of the point cloud is a location in a three-dimensional space, the method comprising steps of: fitting a parameterized surface onto the point cloud formed by N input points p i; wherein predetermined organizational information is input to the fitting step, wherein the organizational information is a specification of a mapping between each input point p i and its location in an organizational matrix, vector, or address in the memory; wherein the N input points p i are arranged and stored into the memory or in the matrix or vector having M elements, locations, or addresses; wherein the arranged input points p i and null point placeholders are stored combined in M locations comprising N input points p i and M - N null point placeholders, where M is larger than N; generating a set of M surface model points fm j, wherein the M surface model points fm j are arranged and stored into M memory locations containing the same number and arrangement of addresses or elements as in said M locations comprising N input points p i and M - N null point placeholders; generating model parameters from the parameterized surface; wherein a surface model of the parameterized surface is represented by the set of points f m j ≜ { fm x j, fm y j, fm z j}, j = {1, 2,..., M}, where each point fm j represents a discrete point on a continuous surface model f x y z ≜ f x f y f z, where (f x, f y, f z) represents the location of the surface model in Cartesian space; computing corresponding points f i i = {1, 2,..., N} having locations on the parameterized surface represented by the set of points fm j by selecting N points from the M surface model points fm j, wherein each corresponding point f i corresponds to each input point p i; wherein the N corresponding points f i, i = {1, 2,..., N} are selected from the M surface model points fm j, j = {1, 2,..., M} such that the selected points f i are the list of surface model points corresponding to locations in the input point memory that contain non-null points; computing residual data based on the corresponding points f i and the input points of the point cloud; compressing the model parameters and the residual data to yield coded model parameters and coded residual data; and producing a bit-stream from the coded model parameters of the parameterized surface and the coded residual data; wherein the step of compressing includes transform and quantization steps. fitting a parameterized surface onto the point cloud formed by N input points p i; wherein predetermined organizational information is input to the fitting step, wherein the organizational information is a specification of a mapping between each input point p i and its location in an organizational matrix, vector, or address in the memory; wherein the N input points p i are arranged and stored into the memory or in the matrix or vector having M elements, locations, or addresses; wherein the arranged input points p i and null point placeholders are stored combined in M locations comprising N input points p i and M - N null point placeholders, where M is larger than N; generating a set of M surface model points fm j, wherein the M surface model points fm j are arranged and stored into M memory locations containing the same number and arrangement of addresses or elements as in said M locations comprising N input points p i and M - N null point placeholders; generating model parameters from the parameterized surface; wherein a surface model of the parameterized surface is represented by the set of points f m j ≜ { fm x j, fm y j, fm z j}, j = {1, 2,..., M}, where each point fm j represents a discrete point on a continuous surface model f x y z ≜ f x f y f z, where (f x, f y, f z) represents the location of the surface model in Cartesian space; computing corresponding points f i i = {1, 2,..., N} having locations on the parameterized surface represented by the set of points fm j by selecting N points from the M surface model points fm j, wherein each corresponding point f i corresponds to each input point p i; wherein the N corresponding points f i, i = {1, 2,..., N} are selected from the M surface model points fm j, j = {1, 2,..., M} such that the selected points f i are the list of surface model points corresponding to locations in the input point memory that contain non-null points; computing residual data based on the corresponding points f i and the input points of the point cloud; compressing the model parameters and the residual data to yield coded model parameters and coded residual data; and producing a bit-stream from the coded model parameters of the parameterized surface and the coded residual data; wherein the step of compressing includes transform and quantization steps.