Surface intersection method
Surface intersection method
 CN 101,980,231 A
 Filed: 11/09/2010
 Published: 02/23/2011
 Est. Priority Date: 11/09/2010
 Status: Active Application
First Claim
1. a surface intersection method is characterized in that, may further comprise the steps:
 A, curved surface is divided into little intersecting area;
B, determine initial point;
C, constructing curve are asked the friendship equation with two unknowns;
D, separate described surface intersection equation with two unknowns;
E, according to the root of described equation with two unknowns structure intersection.
Chinese PRB Reexamination
Abstract
The invention provides a surface intersection method, which comprises the following steps of: dividing surfaces into small crossed areas; determining a starting point; constructing a surface intersection equation in two unknowns; solving the surface intersection equation in two unknowns; and constructing lines of intersection according to roots of the equation in two unknowns. Therefore, the method effectively improves the iteration efficiency, the tracking step length and direction determination precision and the accuracy at the nearly overlapping of the surfaces in the process of performing the surface intersection by utilizing a tracking method.

1 Citation
Data processing method applied to threedimensional geological surface model  
Patent #
CN 105,931,297 A
Filed 04/12/2016

Current Assignee

No References
11 Claims

1. a surface intersection method is characterized in that, may further comprise the steps:

A, curved surface is divided into little intersecting area; B, determine initial point; C, constructing curve are asked the friendship equation with two unknowns; D, separate described surface intersection equation with two unknowns; E, according to the root of described equation with two unknowns structure intersection.


2. surface intersection method according to claim 1 is characterized in that, described steps A comprises substep:

A1, judge that whether curved surface intersects;
, then enter steps A 2 if intersect;
Otherwise process ends;A2, structure intersecting area.


3. surface intersection method according to claim 2 is characterized in that, described steps A 2 comprises following substep:

A2.1, judge whether two curved surfaces are smooth respectively, if then carry out next step, otherwise it is divided into two subcurved surface fragments, and replace this curved surface with these two subcurved surface fragments at the rough place of curved surface; A2.2, judge described curved surface or subsurface normal direction circular cone angle whether all less than On curved surface or the subsurface every border walk around angle whether all less than Whether nonintersect whether two curved surfaces or subsurface normal direction circular cone or its angle all less than certain designated value;
When abovementioned Rule of judgment satisfies simultaneously, then carry out next step;
Otherwise process ends;
A2.3, whether have extreme point and a coordinate system structure intersecting area according to curved surface or subsurface, curved surface or subsurface.


4. surface intersection method according to claim 1 is characterized in that, described step C comprises following substep:

C1, definition dyadic formula value; C2, definition evaluation interval; The root of C3, defining equation; C4, design dyadic formula; C5, the abovementioned iterative formula value of use, evaluation interval, equattion root and dyadic formula are formed described equation with two unknowns.


5. surface intersection method according to claim 4 is characterized in that, described step C4 comprises:

It is that distance is the set of 0 point on the Z coordinate direction that surfaces intersection is defined as at area coordinate; If the direction parameter of first curved surface is u, v, the direction parameter of second curved surface is p, q, S be on first curved surface more arbitrarily, F is a point corresponding with S on second curved surface, S and F relation be;
(SF) * Z=0;If the * Z of the distance D of pointtopoint transmission (S, F point)=(SF), then;


6. surface intersection method according to claim 1 is characterized in that, described step D comprises substep:

D1, according to initial point and corresponding tracking direction thereof that step B obtains, can judgement follow the trail of forward at this initial point place;
if passable, then enter next step;
Otherwise forward step D9 to;D2, determine that current tracking direction is for forward; D3, search the surface intersection zone corresponding;
, then enter next step if find described zone with this initial point according to initial point and current tracking direction;
Otherwise, then forward step D9 to;D4, follow the trail of next point according to initial point;
If track next point, then enter next step;
Otherwise return step D3;D5, the next one point that will track are defined as current point; D6, judge whether current point is the end points of terminating point or described intersecting area;
if then enter next step;
Otherwise return step D4;D7, judge whether current point is initial tracking point;
if not, next step then entered;
Otherwise enter step D14;D8, can judge at initial point place backward tracing;
if can, then enter next step;
Otherwise enter step D14;D9, determine current tracking direction for the back to; D10, search the relevant range;
, then enter next step if find the relevant range according to current point and current tracking direction;
Otherwise, then forward step D14 to;D11, according to the next point of current point tracking;
If track next point, then enter next step;
Otherwise return step D10;D12, the next one point that will track are defined as current point; D13, judge whether current point is the end points of terminating point or described intersecting area;
if then enter next step;
Otherwise return step D11;D14, the root that former and later two tracking directions are all obtained are merged into a root.


7. surface intersection method according to claim 6 is characterized in that, described step D5 comprises following substep:

Steplength is followed the trail of in D5.1, estimation; The tangential direction that D5.2, calculating are followed the trail of; D5.3, estimate next point; The iteration scope of D5.4, the next point of calculating; D5.5, iterate to next point; Whether D5.6, inspection be a bit legal down;
if illegal, then enter next step;
Otherwise, forward step 8 to;D5.7, will follow the trail of steplength and reduce by half, go back to step 5 behind the next point of estimation again; D5.8, end are followed the trail of.


8. surface intersection method according to claim 7 is characterized in that, and is as follows to the estimation of following the trail of steplength among the described step D5.1:
Counting Fv at the single order partial derivative of currency Val is not 0 o'"'"'clock, and the tracking steplength of estimation is;
Counting Fu at the single order partial derivative of currency Val is not 0 o'"'"'clock, and then Gu Suan the steplength of chasing is;
Wherein, the parameter of currency Val is U, V.

9. surface intersection method according to claim 7 is characterized in that, being calculated as follows the tracking tangential direction among the described step D5.2:

If the tracking direction is rV _{t}, the parameter of currency is;
U, V;
If follow the trail of direction for forward, then rV _{t}=(Fv ,Fu);
Otherwise rV _{t}=(Fv, Fu);
If rV _{t}Length be not 0, then with rV _{t}After the unitization, as final tracking tangential direction;
Otherwise, establish discriminant d=Fuv*FuvFuu*Fvv, wherein;
Fu, Fv are the single order partial derivative of currency, and Fuv, Fuu, Fvv are the secondorder partial differential coefficient of currency;
If discriminant d is 0, then current point is deducted the vectorial unitization that previous point obtains after, as final tracking tangential direction; If follow the trail of direction for backward, then rV _{t}=(Fvv, Fuv);
Otherwise rV _{t}=(Fvv ,Fuv);
If the length of rVt is not 0, then with rV _{t}After the unitization, be final tracking tangential direction;
Otherwise after current point deducted the vectorial unitization that previous point obtains, as final tracking tangential direction.


10. surface intersection method according to claim 7 is characterized in that, described step D5.4 comprises following substep:

D5.4.1, scope, all initial points and current some restricted portion, the end points of all wellknown root and asking also of current some restricted portion and current point self restricted portion with current intersecting area. D5.4.2, with described ask and the result as the iteration scope of next one point.


11. surface intersection method according to claim 7 is characterized in that, described step D5.5 comprises following substep:
D5.5.1, the described iterative equation group of definition are as follows;
Specification(s)