Method for designing three-dimensional freeform surface

Patent metadata

Field	Value
Publication number	US-2016232718-A1
Application number	US-201514832503-A
Country	US
Kind code	A1
Filing date	Aug 21, 2015
Priority date	Feb 5, 2015
Publication date	Aug 11, 2016
Grant date	—

Abstract

A method for designing three-dimensional freeform surface is provided. An initial surface and a first three-dimensional rectangular coordinates system are established. A number of feature rays are selected. A number of intersections of the feature rays with a first freeform surface are calculated, wherein the intersections are a number of feature data points. The first freeform surface is obtained by surface fitting the feature data points. An equation of the first freeform surface includes a conic term and a freeform surface term. The first freeform surface is taken as the initial surface for an iteration process.

First claim

What is claimed is:

1 . A method for designing a three-dimensional freeform surface, the method comprising:
step (S 1 ), establishing an initial surface and a first three-dimensional rectangular coordinates system; step (S 2 ), selecting a plurality of feature rays R i (i=1, 2 . . . K); step (S 3 ), calculating a plurality of feature data points P i (i=1, 2 . . . K) of a first freeform surface point by point based on a given object-image relationship or a given light mapping relationship and a vector form of the Snell's law; step (S 4 ), fitting the plurality of feature data points P i (i=1, 2 . . . K) into a sphere in the first three-dimensional rectangular coordinates system; defining a feature data point (x o , y o , z o ) corresponding to a chief ray of a central field angle among an entire field-of-view as a vertex of the sphere; and defining a second three-dimensional rectangular coordinates system by the vertex of the sphere as origin, and a line passing through a center of curvature and the vertex of the sphere as a Z′-axis; step (S 5 ), transforming a plurality of first coordinates (x i , y i , z i ) and a plurality of first normal vectors (α i , β i , γ i ), of the plurality of feature data points P i (i=1, 2 . . . K), in the first three-dimensional rectangular coordinates system into a plurality of second coordinates (x′ i , y′ i , z′ i ) and a plurality of second normal vectors (a′ i , β′ i , γ′ i ) in the second three-dimensional rectangular coordinates system; fitting the plurality of feature data points P i (i=1, 2 . . . K) into a conic surface in the second three-dimensional rectangular coordinates system; removing a plurality of third coordinates and a plurality of third normal vectors of the plurality of feature data points P i (i=1, 2 . . . K), on the conic surface in the second three-dimensional rectangular coordinates system, from the plurality of second coordinates (x′ i , y′ i , z′ i ) and the plurality of second normal vectors (α′ i , β′ i , γ′ i ), to obtain a plurality of residual coordinates and a plurality of residual normal vectors; and surface fitting the plurality of residual coordinates and the plurality of residual normal vectors to obtain a second freeform surface; adding a first equation of the conic surface and a second equation of the second freeform surface to obtain a third equation of the first freeform surface; and step (S 6 ), taking the first freeform surface as the initial surface for an iteration process, to obtain the three-dimensional freeform surface.

2 . The method of claim 1 , wherein the third equation of the first freeform surface is:

z


(

x
,
y

)

=

c


(

x
2

+

y
2

)

1
+

1
-

(

1
+
k

)



c
2



(

x
2

+

y
2

)

+

∑

j
=
1

N





A
j



g
j



(

x
,
y

)

;

wherein,

c


(

x
2

+

y
2

)

1
+

1
-

(

1
+
k

)



c
2



(

x
2

+

y
2

)

is a conic term, c is a curvature of the conic surface at the vertex, k is a conic constant;

Assignees

• Univ Tsinghua
• Hon Hai Prec Ind Co Ltd

Inventors

• Zhu Jun
• Yang Tong
• Wu xiao-fei
• Jin Guo-Fan
• Fan Shou-Shan

Classifications

• G06T2219/2021

  Shape modification · CPC title

• G06T19/20 Primary

  Editing of three-dimensional [3D] images, e.g. changing shapes or colours, aligning objects or positioning parts · CPC title

• G06T17/00 Primary

  Three-dimensional [3D] modelling for computer graphics · CPC title