CN102147934A - Geological interface three-dimensional morphological analysis method based on TIN (triangulated irregular network) - Google Patents

Abstract

The invention discloses a geological interface three-dimensional morphological analysis method based on TIN (triangulated irregular network), which comprises the following steps: based on the use of a three-dimensional TIN model to simulate the geological interface, using the principles of space geometry and computer graphics to calculate general geometrical morphology parameters (gradient, angle and the like) and distance fields of the geological interface; using space interpolation and trend residual analysis technology to extract the morphology trend and fluctuation of the geological interface in a grading way; and finally applying a geological interface three-dimensional morphological analysis result to the simulation of ore-controlled geological factor fields and the concealed ore body forecasting. The method can precisely and efficiently analyze and extract all morphology parameters of the geological interface and expresses ore-controlled geological factors quantificationally and has significance in concealed ore body three-dimensional quantitative forecasting.

Description

Geological interface three-dimensional configuration analytical approach based on TIN

Technical field

The present invention relates to a kind of geological interface three-dimensional configuration analytical approach based on TIN.TIN refers to Triangulated IrregularNetwork, TIN.

Background technology

Control ore deposit geologic agent can't effectively be obtained and express to the traditional GIS spacial analytical method.And the geologic body three-dimensional configuration analytical approach that proposes in conjunction with mathematical morphology based on the three-dimensional geologic Raster Data Model (Deng Hao is towards three-dimensional geological modeling and the some technical research of the spatial analysis Changsha of concealed orebody prediction: (mao XianCheng Central South University 2008), Tang Yanhua, the three-dimensional configuration analysis of Deng Hao geologic body and method Central South University journal (natural science edition), 2011), have following shortcoming: raster data model space data volume is big, the low spatial precision, can not accurately express the border of geologic body during particularly to boundary representation, and formation speed, storage space and expression precision are difficult to balance; The quantification aspect that is chosen at of mathematical morphology spherical structure element radius needs to improve; Be not suitable for laminar geologic body or exist the geologic body of narrow to carry out the trend model analysis, when the structural element radius is big, the mistake that trend model can occur rupturing, this is because the narrow positions of geologic body can weed out because of filtering operation rises and falls as the part, thereby ruptures.

Summary of the invention

Technical matters to be solved by this invention is to propose a kind of geological interface three-dimensional configuration analytical approach based on TIN, should can extract the various morphological parameters of geological interface based on the geological interface three-dimensional configuration analytical approach of TIN more accurate, more efficiently, effectively quantification is expressed control ore deposit geologic agent.

Technical solution of the present invention is as follows:

A kind of geological interface three-dimensional configuration analytical approach based on TIN, may further comprise the steps: using three-dimensional TIN model to simulate on the basis of geological interface, how much of usage spaces and computer graphics principle are calculated the general geometry parameter and the distance field of geological interface; Form trend and the form of utilizing space interpolation and trend residual analytical technology grading extraction to go out geological interface rise and fall.

Described general geometry parameter comprises the gradient and angle;

(1) computing method of the gradient are: in three-dimensional TIN model, (plane equation is any triangle ABC: z=a ₀+ a ₁X+a ₂The coordinate on three summits y) is A (x ₁, y ₁, z ₁), B (x ₂, y ₂, z ₂), C (x ₃, y ₃, z ₃), the gradient of triangle ABC is:

$S=\arccos \frac{1}{\sqrt{a_1^2+a_2^2+1}}$

Wherein, $a_1=\frac{(y_2-y_1)*(z_3-z_1)-(y_3-y_1)*(z_2-z_1)}{(x_3-x_1)*(y_2-y_1)-(x_2-x_1)*(y_3-y_1)},$ $a_2=\frac{(x_3-x_1)*(z_2-z_1)-(x_2-x_1)*(z_3-z_1)}{(x_3-x_1)*(y_2-y_1)-(x_2-x_1)*(y_3-y_1)};$

(2) computing method of angle are:

Described angle refers to the angle of certain point on two bed boundary intersections, promptly passes through the angle between two tri patchs of this point, and method is as follows:

Be the unit to form a plurality of blocks unit at first with the geological interface rasterizing, promptly adopt the three-dimensional regular grid that the study area geological space is divided into many small cubes, the tri patch that passes the same block body unit in two geological interface TIN models is asked angle in twos, at last with the mean value of the angle of trying to achieve as the angle α between the geological interface ^*, angle α ^*Ask method as follows:

If two leg-of-mutton normal vectors are divided into V ₁(x _V1, y _V1, z _V1), V ₂(x _V2, y _V2, z _V2), the angle of two normal vectors is α, i.e. angle between two tri patchs, and the formula of calculating is:

$\cos \mathrm{\α}=\frac{V_1\·V_2}{\left|V_1\right|\left|V_2\right|}=\frac{x_{v1}*x_{v2}+y_{v1}*y_{v2}+z_{v1}*z_{v2}}{\sqrt{{x_{v1}}^2+{y_{v1}}^2+{z_{v1}}^2}\sqrt{{x_{v2}}^2+{y_{v2}}^2+{z_{v2}}^2}}$

$\mathrm{\α}=\arccos \frac{x_{v1}*x_{v2}+y_{v1}*y_{v2}+z_{v1}*z_{v2}}{\sqrt{{x_{v1}}^2+{y_{v1}}^2+{z_{v1}}^2}\sqrt{{x_{v2}}^2+{y_{v2}}^2+{z_{v2}}^2}}$

The angle α between the geological interface then ^*Expression formula be:

Wherein n equals the angle number of the tri patch of two geological interfaces in same block unit.

Some metallogenic factors are subjected to the angle of geological interface and the control of gradient size, and general geometry parameters such as the geological interface angle and the gradient are extracted can this control of quantitative expression ore deposit factor, have vital role for excavating favourable one-tenth ore deposit information.Follow-up being put in the instructions by me of-this section gone.

The computing method of distance field are:

Certain puts the distance dependent of the geological interface that is associated in control geologic agent field, ore deposit and the space, and promptly controlling geologic agent field, ore deposit is certain spatially distributed functions of putting the geological interface distance in the space,

Find the solution to the minimum distance of geological interface the unit, is actually to seek unit center and put the minimum value of geological interface TIN apart from set; The TIN model is made up of many tri patchs, is actually a little to the unilateral bee-line of all triangles so put the distance of geological interface;

Obtaining the prediction space is the distance value of each unit correspondence in the aforesaid study area geological space, set up the distance field model, the minimum value [unit has only a distance value] of the central point that described distance value refers to some unit distance value of each tri patch in the TIN model.

Form trend and form fluctuating that grading extraction goes out geological interface comprise:

What the space trend model reflected is the body feature of space object on area of space, and it has been ignored local form and has risen and fallen to disclose the body feature on the area of space.In the geology of mineral deposit space, the subject form of plastid will play the influence of certain factor to becoming the ore deposit on every side relatively, and rising and falling then is the side reflection of geologic anomaly effect.Therefore, the analysis of plastide morphology (the geologic body form i.e. the form of the geological interface of this geologic body correspondence) will be the important step of control ore deposit factor dose over the ground.

The form trend of described geological interface is meant the new TIN model that new summit that the Z value on the summit of the tri patch in the geological interface TIN model is obtained according to square distance inverse ratio method assignment is again set up, new TIN model is called the trend surface of geological interface, and the forming process of the trend surface of geological interface is as follows:

1. determine that detection range d (determine according to the exploratory line engineering spacing by the size of d, if the exploratory line engineering spacing is 100 meters, then the d of one-level trend analysis gets 100 meters, the d of secondary trend analysis gets 2 times of engineering spacings, then be 200 meters), have only with estimation point distance and (describe actual sampled data points with the summit of TIN intermediate cam shape less than the sample spot of d, sample spot is actual sampled data points herein, also be vertex of a triangle) could participate in calculating, its middle distance is meant at 2 in the distance between subpoint on the XY plane, rather than 2 absolute distance; The estimation point refers to the subpoint of any one summit on the XY plane in the original geological interface TIN model; Set up the process of new TIN model, exactly all estimation points are all calculated the z value that makes new advances, form the summit of new TIN model, make up new TIN model according to this summit again.

2. utilize square distance inverse ratio method to recomputate all z values of sample spot, formula is as follows:

$z=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{z_i}{d_i^2}}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{1}{d_i^2}}$

Wherein, z _iRepresent around this estimation point, with the vertical coordinate component of estimation point distance less than the sample spot of d; d _iThe distance of representing this estimation point and sample spot; Distance all refers at 2 in the distance between subpoint on the XY plane herein;

3. utilize the z value of calculating, (new geological interface TIN model adopts x, the y coordinate of former TIN model vertices collection, makes new summit with the corresponding z coordinate of new calculating, and the limit collection is constant to set up new geological interface TIN model, topological structure is constant), the trend surface of formation geological interface;

According to the method described above, adopt different detection range d (the filtering rank is generally 2 grades, and distance can be got 1d and 2d respectively), get final product the form trend that grading extraction obtains geological interface;

Described form rises and falls and is meant the relief intensity (be also referred to as wave amplitude) of geological interface with respect to the form trend surface, and promptly the z value in the geological interface deducts the z value of form trend surface, can obtain form and rise and fall.Because the extraction of the form trend of geological interface is classification, so it also is classification that form rises and falls.

By aforesaid method, obtained the control ore deposit geologic agent index of three broad aspect such as the classification form trend of general geometry parameter (gradient, angle etc.), distance field, geological interface of geological interface and the fluctuating of classification form.

Beneficial effect:

The invention discloses a kind of based on TIN (Triangulated Irregular Network, TIN) geological interface three-dimensional configuration analytical approach, be included in and use three-dimensional TIN model to simulate on the basis of geological interface, how much of usage spaces and computer graphics principle are calculated the general geometry parameter (gradient of geological interface, angle etc.) and distance field, utilize space interpolation and trend residual analytical technology, form trend and form that grading extraction goes out geological interface rise and fall, at last, geological interface three-dimensional configuration analysis result is applied to control the simulation and the concealed orebody prediction of geologic agent field, ore deposit.The present invention is based on the TIN model, but the TIN model has advantages such as adapt to any form curved surface, express the precision free adjustment, be suitable for sparse data, modeling speed is fast, therefore, the present invention can bring into play the advantage of TIN model, can analyze and extract the various morphological parameters of geological interface accurately, efficiently, express control ore deposit geologic agent quantitatively, for the three-dimensional quantitative forecast of concealed orebody is provided as ore deposit information foundation.

Description of drawings

Fig. 1 is the geological interface three-dimensional configuration analysis process figure based on TIN;

Fig. 2 is unconformity surface gradient factor (gU) distribution grid model synoptic diagram (150 meters to-200 meters absolute altitude scopes);

Fig. 3 is angle factor (aU_S) the distribution grid model synoptic diagram (150 meters to-200 meters absolute altitude scopes) of bed boundary and unconformity surface;

Fig. 4 is unconformity surface distance factor (dU) distribution grid model synoptic diagram (150 meters to-200 meters absolute altitude scopes)

Fig. 5 is unconformity surface master mould and trend model model synoptic diagram, (a) the three-dimensional TIN model synoptic diagram of unconformity surface; (b) the interpolation search radius is 100 meters a unconformity surface one-level trend TIN model synoptic diagram;

Fig. 6 is a unconformity surface form fluctuating grading extraction synoptic diagram, (a) one-level evagination female parts; (b) secondary evagination female parts;

Fig. 7 is unconformity surface form fluctuating factor (waU and wbU) distribution grid model synoptic diagram (150 meters to-200 meters absolute altitude scopes), (a) one-level fluctuating waU; (b) secondary fluctuating wbU.

Embodiment

Below with reference to accompanying drawing and concrete embodiment the present invention is described in further details:

A kind of geological interface three-dimensional configuration analytical approach based on TIN, comprise: using three-dimensional TIN model to simulate on the basis of geological interface, how much of usage spaces and computer graphics principle are calculated the general geometry parameter (gradient, angle etc.) and the distance field of geological interface, utilize space interpolation and trend residual analytical technology, form trend and form that grading extraction goes out geological interface rise and fall, express control geologic agent field, ore deposit with Raster Data Model at last, realize the quantitative simulation of various controls ore deposit geologic agent.1, the geological interface three-dimensional configuration analytical approach based on TIN according to claim 1 is characterized in that, the general geometry parameter (gradient, angle etc.) that how much of described usage spaces and computer graphics principle are calculated geological interface comprising:

(1) gradient is extracted

Because the calculating of the gradient all is based on the TIN model of geological interface, therefore calculates and ask this to put the gradient of pairing tri patch in fact for the gradient of set point.Detailed process is as follows:

Arbitrary triangle ABC can represent with following plane equation on the TIN model:

z＝a ₀+a ₁x+a ₂y (1)

The plane upgrade equates everywhere, can calculate this leg-of-mutton gradient with following formula:

$\text{S=arccos}\frac{1}{\sqrt{a_1^2+a_2^2+1}}---\left(2\right)$

As long as therefore calculate a ₁, a ₂Just can calculate the gradient.

If the coordinate on three summits of triangle ABC is A (x ₁, y ₁, z ₁), B (x ₂, y ₂, z ₂), C (x ₃, y ₃, z ₃), then the normal vector perpendicular to this triangle projective planum is:

If have on the triangle projective planum point M (x, y, z), then

Can draw the equation on plane, triangle place by formula (3):

$\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0---\left(4\right)$

Can draw in conjunction with formula (1) and formula (4):

$a_1=\frac{(y_2-y_1)*(z_3-z_1)-(y_3-y_1)*(z_2-z_1)}{(x_3-x_1)*(y_2-y_1)-(x_2-x_1)*(y_3-y_1)}---\left(5\right)$

$a_2=\frac{(x_3-x_1)*(z_2-z_1)-(x_2-x_1)*(z_3-z_1)}{(x_3-x_1)*(y_2-y_1)-(x_2-x_1)*(y_3-y_1)}---\left(6\right)$

Last substitution formula (2) just can be obtained S.

The S that tries to achieve is exactly the grade information corresponding to each tri patch.

(2) angle extracts between geological interface

Because geological interface all is to adopt the TIN model to carry out modeling, institute is exactly to ask the angle that passes through between two tri patchs of this point in the hope of the angle of certain point on two bed boundary intersections.This method is at first with the geological interface rasterizing, and then asks crossing cubic units, asks the angle between the geological interface at last.

The geological interface rasterizing:

Geological interface is with the TIN model tormulation, and the essence of its rasterizing is exactly that the block unit that geological interface TIN passes is extracted, and forms the Block Model of geological interface.Concrete steps are as follows:

1. tri patch projection.At first with three summits of tri patch to three coordinate planes: projection is carried out on XY plane, XZ plane and YZ plane, obtains three projection triangles.Be example with the XY plane below, the triangle of establishing after the projection is ABC.

2. obtain minimum outsourcing rectangle.Calculate leg-of-mutton minimum outsourcing rectangle EFGH according to leg-of-mutton three summits on projecting plane, this outsourcing rectangle is different with traditional outsourcing rectangle, must coincide with the mesh lines of mineral deposit Block Model in the respective planes projection.The purpose of outsourcing rectangle is to reduce the hunting zone, improves counting yield.

3. calculate triangular trajectory grid on the projecting plane.Adopt the Liang Barsky parametrization line clipping polygon algorithm in the computer graphics, calculate the plane grid that three sides of a triangle pass.But, when triangle is projected as a straight-line segment, and with the mineral deposit Block Model when the mesh lines of respective planes projection overlaps, think that then leg-of-mutton limit is passed on the plane grid is this projection straight line section left and right sides grid (perhaps grid) up and down.

4. fill triangle.Adopt scan-line algorithm to calculate the grid index (i of triangle ABC inside on the XY plane _x, j _y).

5. the grid index on three projecting planes is asked friendship.Similar with the processing on the XY plane, try to achieve the projection of TIN model intermediate cam dough sheet on XZ plane and YZ plane respectively according to top step, and calculate corresponding inner mesh index, then the component of the grid index on three projecting planes is asked friendship, try to achieve the index of the block unit that tri patch passes through at last, and the leg-of-mutton ID that will pass the block unit notes.

6. pass through all the tri patch cycle calculations in the geological interface TIN model, can obtain the block unit that geological interface passes through (adopts the three-dimensional regular grid that the study area geological space is divided into many small cubes, small cubes is called stereo-unit, or claims unit, volume elements, block.), generate the geological interface Block Model at last.

The calculating of angle:

At first the Block Model of two bed boundaries is asked friendship, its essence is exactly to calculate the index value of the block unit that overlaps in the Block Model, record passes the sign ID value of the tri patch that overlaps the block unit simultaneously, calculates the angle between the tri patch that passes same block unit then.Wherein, need carry out special processing to a kind of situation: when the block unit of intersection is the summit of tri patch, the TIN model of geological interface just has a plurality of tri patchs and passes corresponding block unit simultaneously, in this case, the tri patch that passes the same block body unit in two geological interface TIN models is asked angle in twos, at last with the mean value of these angles as end product.

Two leg-of-mutton angles calculate and often adopt vector methods, at first stipulate leg-of-mutton normal vector upwards, and promptly the z component of normal vector is more than or equal to 0, if z less than 0, then important negate; Ask two leg-of-mutton normal vectors then, the cross product of the vector on promptly leg-of-mutton two limits.The angle of normal vector is the angle on two planes.

If two leg-of-mutton normal vectors are divided into V ₁(x _V1, y _V1, z _V1), V ₂(x _V2, y _V2, z _V2), the angle of two normal vectors is α, then:

$\cos \mathrm{\α}=\frac{V_1\·V_2}{\left|V_1\right|\left|V_2\right|}=\frac{x_{v1}*x_{v2}+y_{v1}*y_{v2}+z_{v1}*z_{v2}}{\sqrt{{x_{v1}}^2+{y_{v1}}^2+{z_{v1}}^2}\sqrt{{x_{v2}}^2+{y_{v2}}^2+{z_{v2}}^2}}---\left(7\right)$

$\mathrm{\α}=\arccos \frac{x_{v1}*x_{v2}+y_{v1}*y_{v2}+z_{v1}*z_{v2}}{\sqrt{{x_{v1}}^2+{y_{v1}}^2+{z_{v1}}^2}\sqrt{{x_{v2}}^2+{y_{v2}}^2+{z_{v2}}^2}}---\left(8\right)$

Then the angle between the geological interface is α ^*(wherein n equals the angle number of the tri patch of two geological interfaces in same block unit):

${\mathrm{\α}}^{*}=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i}{n}$

The assignment of angle:

Rapid by previous step, obtained the block set of two bed boundary intersections, and the block in this set has comprised both angle information.Therefore, for the stereo-unit in the whole geological space just by ask for the set of above-mentioned block in the minimum distance of block obtain corresponding angle information.

Because the crossing block set limited amount that obtains, thus adopt the violence algorithm just can ask for fast stereo-unit central point in the geological space gather to this block in the bee-line of block unit central point.The angle information of the pairing block of bee-line is exactly the angle of the required assignment of this stereo-unit in the block set of trying to achieve.

The computing method of distance field are:

Certain puts the distance dependent of the geological interface that is associated in control geologic agent field, ore deposit and the space, promptly controls geologic agent field, ore deposit and be the spatially distributed functions to the geological interface distance.In geological space, this research selects Euclidean distance as space length.Certain puts the distance of geological interface in distance between the geological interface or the geological space, in order to the geometry degree of closeness between expression and the geologize interface or geological interface to the influence degree of certain point in the space.Under study for action, the distance that we will put geological interface is decided to be the minor increment that a little arrives geological interface approximately, predicts that promptly certain unit (volume elements) arrives the minimum distance of geological interface as the influence degree of control geologic agent field, ore deposit to the unit in the space.

By aforementioned, it is that three-dimensional TIN model is described that geological interface can adopt the trivector model, and therefore, find the solution to the minimum distance of geological interface the unit, is actually to seek unit center and put geological interface TIN apart from the minimum value of gathering.Ask the calculating of any one spatial point and arbitrary physical distance, the simplest method is to carry out distance measurements and calculate having a few the central point of unit in the study area geological space (refer to a little) in the geological space, finds out the point of its middle distance minimum.The TIN model is made up of many tri patchs, is actually a little to the unilateral bee-line of all triangles so put the distance of geological interface.From mathematics, in fact be exactly to ask the bee-line that a little arrives face, but because actual conditions, need to consider following two kinds of situations: the intersection point of 1. putting triangular facet drops in the triangular facet; 2. put the intersection point of triangular facet outside triangular facet.Therefore, the matter of utmost importance of putting geological interface is to judge that intersection point is whether in triangle.

If a some P and a triangle ABC are arranged in the space, establishing the coordinate that P orders is (x ₀, y ₀, z ₀), the A point coordinate is (x ₁, y ₁, z ₁), the B point coordinate is (x ₂, y ₂, z ₂), the coordinate (x that C is ordered ₃, y ₃, z ₃).The normal vector on plane, triangle ABC place (l, m n) can be obtained by following formula:

$l=\left|\begin{array}{ccc}1& y_1& z_1\\ 1& y_2& z_2\\ 1& y_3& z_3\end{array}\right|=\left|\begin{array}{cc}{y}_2-y_1& z_2-z_1\\ y_3-y_1& z_3-z_1\end{array}\right|=(y_2-y_1)(z_3-z_1)-(y_3-y_1)(z_2-z_1)---\left(9\right)$

$m=\left|\begin{array}{ccc}{x}_1& 1& z_1\\ x_2& 1& z_2\\ x_3& 1& z_3\end{array}\right|=\left|\begin{array}{cc}{z}_2-z_1& x_2-x_1\\ z_3-z_1& x_3-x_1\end{array}\right|=(z_2-z_1)(x_3-x_1)-(z_3-z_1)(x_2-x_1)---\left(10\right)$

$n=\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|=\left|\begin{array}{cc}{x}_2-x_1& y_2-y_1\\ x_3-x_1& y_3-y_1\end{array}\right|=(x_2-x_1)(y_3-y_1)-(x_3-x_1)(y_2-y_1)---\left(11\right)$

The equation on plane, triangle ABC place is

lx+my+nz＝lx ₁+my ₁+nz ₁ (12)

By P (x ₀, y ₀, z ₀) point perpendicular to the parametric form equation of the straight line on plane, triangle ABC place is

$\left\{\begin{array}{c}x=x_0+\mathrm{tl}\\ y={\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA0000056119650000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+\mathrm{tm}\\ z={\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA0000056119650000031.png"\; state="\{\{state\}\}">z</figure-callout>}}_0+\mathrm{tn}\end{array}\right.---\left(13\right)$

Bring the equation on plane, ABC place into following formula, can solve

$t=\frac{l(x_1-x_0)+m(y_1-y_0)+n(z_1-z_0)}{l^2+m^2+n^2}---\left(14\right)$

The vertical line equation that this t substitution is done to plane, triangle ABC place from the P point again, just can in the hope of the coordinate of intersection point Q (X, Y, Z) as follows:

$\left\{\begin{array}{c}X=x_0+\mathrm{tl}\\ Y={\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA0000056119650000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_0+\mathrm{tm}\\ Z={\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="HDA0000056119650000031.png"\; state="\{\{state\}\}">z</figure-callout>}}_0+\mathrm{tn}\end{array}\right.---\left(15\right)$

Be exactly to judge whether intersection point Q drops in the closed region that three limits of triangle ABC surround below.L, m has at least one to be not equal to 0 among the n, might as well establish n ≠ 0, calculates successively

$\left|\begin{array}{ccc}X& Y& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right|,\left|\begin{array}{ccc}{x}_1& y_1& 1\\ X& Y& 1\\ x_3& y_3& 1\end{array}\right|,\left|\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ X& Y& 1\end{array}\right|$

Just in time equal the absolute value of n if the absolute value of these three values is added up, just illustrate that intersection point Q drops in the closed region that three limits of triangle ABC surround.At this moment, the P point is exactly the vertical range of P point to plane, triangle ABC place, the just length of line segment PQ to the bee-line of triangle ABC

$\mathrm{PQ}=\sqrt{{(X-x_0)}^2+{(Y-y_0)}^2+{(Z-z_0)}^2}---\left(16\right)$

If

The absolute value sum be not equal to the absolute value of n, illustrate that intersection point Q does not drop in the closed region that triangle ABC three limits surround.At this moment, ask the bee-line of P point respectively, get wherein the shortest person then to line segment AB, BC and CA.Bee-line in the hope of P point line segment AB is an example, and detailed process is as follows:

1. judge that whether angle PAB is the obtuse angle or is the right angle, method for the dot product of judging vectorial AP and vectorial AB whether smaller or equal to 0, promptly If satisfy this condition, then P is line segment PA to line segment AB bee-line.

$\mathrm{PA}=\sqrt{{(x_1-x_0)}^2+{(y_1-y_0)}^2+{(z_1-z_0)}^2}---\left(17\right)$

If do not satisfy Then forwarded for following the 2. step to.

2. judge whether angle PAB is obtuse angle or right angle, and process is 1. identical.

3. ought be 1. and 2. condition do not satisfy, then the P point is positioned at line segment AB inside to the intersection point of line segment AB, establish intersection point Q (Z), the parametric equation of straight line AB can be written as for X, Y:

$\left\{\begin{array}{c}x=t(x_2-x_1)+x_1\\ y=t(y_2-y_1)+y_1\\ z=t(z_2-z_1)+z_1\end{array}\right.---\left(18\right)$

Then vectorial PQ can be expressed as: (x ₁+ t (x ₂-x ₁)-x ₀, y ₁+ t (y ₂-y ₁)-y ₀, z ₁+ y (z ₂-z ₁)-z ₀)

Vector AB is: (x ₂-x ₁, y ₂-y ₁, z ₂-z ₁)

Because vectorial AB is vertical with vectorial PQ, then Therefore can in the hope of

$t=\frac{(x_1-x_2)*(x_1-x_0)+(y_1-y_2)*(y_1-y_0)+(z_1-z_2)*(z_1-z_0)}{(x_1-x_2)*(x_1-x_2)+(y_1-y_2)*(y_1-y_2)+(z_1-z_2)*(z_1-z_2)}---\left(19\right)$

Parametric t is updated to formula (18), just can obtains the coordinate of intersection point point Q, obtain the length of PQ then.

Can calculate each unit in the geological space by this distance algorithm programming to TIN, promptly the stereo-unit central point utilizes the distribution of this distance in geological space to realize the discretize modeling of control geologic agent field, ore deposit to the minimum distance of geological interface.

Form trend and form fluctuating that described space interpolation and the trend residual analytical technology utilized, grading extraction go out geological interface comprise:

Use for reference the trend model analytical approach of traditional curved surface,, adopt the original TIN model of geological interface, utilize square distance inverse ratio method that geological interface is carried out the trend model analysis in conjunction with the actual conditions of geological interface.

In fact the trend model analysis of geological interface TIN model be exactly to utilize the sample spot within the certain distance around the estimation point to the z value of estimation point assignment again, utilizes the trend surface of the new z value generation geological interface that calculates then.Detailed process is as follows:

1. determine detection range d, have only with the sample spot of estimation point distance could participate in calculating that its middle distance is meant 2 relative distances on the XY plane, rather than 2 absolute distance less than d.

2. utilize square distance inverse ratio method to recomputate all z values of sample spot, formula is as follows:

$z=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{z_i}{d_i^2}}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{d_i^2}}---\left(20\right)$

3. utilize the z value of calculating, set up the TIN model of new geological interface, form the trend surface of geological interface.

The geologic body rolling shape can be described by the undulation of geological interface.This undulation can be expressed with respect to the relief intensity on its trend plane by geological interface.This relief intensity is wave amplitude again, the degree of crook of reflection geological interface and the undulation changes in amplitude in the space.

This sinuous modeling can realize by previously described trend model analysis, and the variation that is about to the observed reading of geological interface absolute altitude z is decomposed into two parts: 1. observed reading totally changes a curved surface of reconstruction, promptly trend surface T (x, y); 2. the localized variation of observed reading, appellation is a signal, promptly remain trend surface R (x, y); Promptly

z(x，y)＝T(x，y)+R(x，y) (21)

Then remain trend surface R (x, y):

R(x，y)＝z(x，y)-T(x，y) (22)

For on the geology curved surface a some z (x ₀, y ₀), can pass through R (x, y) absolute value is described this form fluctuating quantity of putting residing part, by R (x, symbol y) describe this to put residing part be evagination or indent, and be still smooth, has:

For R (x, y) represented part rises and falls, and can be considered the stack that different stage rises and falls, and has:

R(x，y)＝R ₁(x，y)+R ₂(x，y)+...+R _n(x，y) (24)

Wherein, R ₁(x, y), R ₂(x, y). .., R _n(x y) has represented the local fluctuations of n level, the available trend residual analytical approach of the screening of localized variation at different levels.

Utilize said method can realize the grading extraction that form rises and falls.But because the size of the waveform of interpolation search radius d decision filtering, so by changing the fluctuating that the d value can extract different stage.Algorithm at first carries out shape filtering with the less interpolation search radius of d value to geologic body, extracts first order trend model and less fluctuating; Then increase the d value,, further draw second level trend model and rise and fall than the upper level bigger new one-level that do not rise and fall to first order trend model shape filtering once more; Increase the d value once more, the other trend model of upper level is carried out a new shape filtering, the one-level that must make new advances trend model and fluctuating; Iteration is gone down so always, till the d value reaches the appointment max-thresholds.The d value changes, and trend just changes; Trend changes, and corresponding fluctuating has just changed

The residue trend surface of geological interface has reflected the fluctuations degree of geological interface in the space well by wave amplitude, wave amplitude for any point on the quantitative description geological interface, need to calculate on geological interface and the trend surface and have identical x, the difference of the z coordinate of the point of y value, come down to by x, y calculates the z value of geological interface and trend surface.Computation process is as follows:

Arbitrary triangle ABC in the geological interface TIN model, known A (x ₁, y ₁, z ₁), B (x ₂, y ₂, z ₂), C (x ₃, y ₃, z ₃), the arbitrfary point M in the plane, triangle ABC place (z), plane equation is for x, y:

$\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0---\left(25\right)$

Solve: $z=\frac{(z_2-z_1)(y_3-y_1)(x-x_1)+(y-y_1)(x_2-x_1)(z_3-z_1)-(x-x_1)(y_2-y_1)(z_3-z_1)-(y-y_1)(z_2-z_1)(x_3-x_1)}{(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)}+z_1---\left(26\right)$

But as triangle ABC during perpendicular to the XY plane, identical x, it is corresponding that the y value has numerous z value, for this kind situation, with z be defined as minimum value and maximal value and half, that is:

$z=\frac{z_{\max }+z_{\min }}{2}---\left(27\right)$

Embodiment 1:

Below six steps describe based on the geological interface morphological analysis method of TIN and implement, be example with the unconformity surface of Youxi County Ding Jia mountain, Fujian Province lead-zinc deposit.

(1) set up unconformity surface TIN model and mineralising space lattice model: utilize Datamine software unconformity surface on the geologic section (when up and down interruption in deposition or lost strata occurring between the two cover different times stratum, this two cover contact interface between stratum is called unconformity surface) known location point (the known location point is meant the reference mark of the unconformity surface position that technological means such as utilizing face of land charting, exploration engineering, underworkings is obtained) couple together with line, form a series of line segments, utilize the wire-frame model modeling function to set up the TIN model of unconformity surface then.The TIN model is stitched together these line segments and forms a triangular mesh and simulate geological interface with the form of tri patch, and exports to the Access database.The employing precision is the stereo-unit lattice of 10m * 10m * 10m, divides the mineralising space, forms the Raster Data Model in mineralising space.Raster Data Model is stored in the Access database, and simultaneously, three-dimensional configuration analysis result and control ore deposit factor index extract the result and also be stored in this database.

(2) geological interface three-dimensional configuration analysis software TriangelCal exploitation: adopt C# language, under VisualStudio 2005 platforms, utilize the embodiment described in the content of the present invention (formula (1) is to formula (27)) design and exploitation geological interface three-dimensional configuration analysis software TriangelCal, comprise five functional modules: 1. model data read module; 2. geological interface distance field computing module; 3. geological interface general geometry parameter extraction module; 4. geological interface trend-fluctuating analytical calculation module; 5. the result preserves module.Below each step be that step (3) to step (5) all adopts this software to calculate.

(3) distance field of geological interface calculates: with the unit to the minor increment of unconformity surface as the distance field value, i.e. unconformity surface distance field factor index dU.Formula (14) and formula (15) are tried to achieve the intersection point coordinate of stereo-unit central point to geological interface, judge intersection point then whether in triangle, try to achieve distance under the different situations respectively according to formula (16) and formula (17) then.For distinguishing the difference of the distance field value of lower unit on the unconformity surface, the unit field value that will be positioned on the unconformity surface distribution range just is being changed to (positive distance field), and the unit field value that is positioned under the unconformity surface distribution range is negative (negative distance field).

(4) the general geometry parameter of geological interface (gradient, angle etc.) is extracted: utilize formula (5) and formula (6) to obtain the triangle projective planum equation parameter, be updated to formula (2) and obtain unconformity surface gradient factor gU; When asking unconformity surface angle factor aU_S, earlier to unconformity surface and other geological interface rasterizings, and try to achieve common factor, utilize formula (7) and formula (8) to try to achieve the average angle of geological interface intersection then, because it is crossing that unconformity surface and a plurality of bed boundary have, the unconformity surface angle desired value value of definition unit is the nearest angle of unit to the minimum distance place correspondence of unconformity surface.

(5) grading extraction goes out the form trend and the form fluctuating of geological interface: the interpolation search scope radius of selecting 100m and 200m, according to square distance inverse ratio method is formula (20), the original TIN model of unconformity surface is carried out one-level shape filtering and secondary shape filtering, obtain one-level trend and one-level fluctuating waU, secondary trend and the secondary fluctuating wbU of unconformity surface respectively.

(6) application of geological interface three-dimensional configuration analysis result: will be stored in the three-dimensional configuration analysis result in the Raster Data Model Access database, import Datamine software, form the Block Model of control ore deposit geologic agent, utilize the block visualization function of Datamine, finish the visual expression of control ore deposit geologic agent; Known mineralising index in the Access database and control ore deposit geologic agent index are carried out regretional analysis, set up the ore body forecast model and (set up the concealed orebody three-dimensional quantitative forecast model of reflection control ore deposit index to the Nonlinear Mapping relation of mineralising distribution, comprise and be used for the predicting unit grade, the multivariate regression model of amount of metal and the logistic regression model that is used to predict ore-bearing potential, control ore deposit geologic agent index substitution model with unknown elements, can reach grade to the unknown elements chats, amount of metal, the purpose that the ore-bearing potential index is predicted), it is 123917.37 tons that prediction obtains plumbous distant view amount of metal, and the distant view amount of metal of zinc is 520334.04 tons.Predicting the outcome can be by implementing to look for miner Cheng Jinhang checking.

Claims (2)

1. geological interface three-dimensional configuration analytical approach based on TIN, it is characterized in that, may further comprise the steps: using three-dimensional TIN model to simulate on the basis of geological interface, how much of usage spaces and computer graphics principle are calculated the general geometry parameter and the distance field of geological interface; Form trend and the form of utilizing space interpolation and trend residual analytical technology grading extraction to go out geological interface rise and fall.

2. the geological interface three-dimensional configuration analytical approach based on TIN according to claim 1 is characterized in that described general geometry parameter comprises the gradient and angle;

(1) computing method of the gradient are: in three-dimensional TIN model, the coordinate on three summits of any triangle ABC is A (x ₁, y ₁, z ₁), B (x ₂, y ₂, z ₂), C (x ₃, y ₃, z ₃), the gradient of triangle ABC is:

$S=\arccos \frac{1}{\sqrt{a_1^2+a_2^2+1}}$

Wherein, $a_1=\frac{(y_2-y_1)*(z_3-z_1)-(y_3-y_1)*(z_2-z_1)}{(x_3-x_1)*(y_2-y_1)-(x_2-x_1)*(y_3-y_1)},$ $a_2=\frac{(x_3-x_1)*(z_2-z_1)-(x_2-x_1)*(z_3-z_1)}{(x_3-x_1)*(y_2-y_1)-(x_2-x_1)*(y_3-y_1)};$

(2) computing method of angle are:

Described angle refers to the angle of certain point on two bed boundary intersections, promptly passes through the angle between two tri patchs of this point, and method is as follows:

Be the unit to form a plurality of blocks unit at first with the geological interface rasterizing, promptly adopt the three-dimensional regular grid that the study area geological space is divided into many small cubes, the tri patch that passes the same block body unit in two geological interface TIN models is asked angle in twos, at last with the mean value of the angle of trying to achieve as the angle α between the geological interface ^*, angle α ^*Ask method as follows:

If two leg-of-mutton normal vectors are divided into V ₁(x _V1, y _V1, z _V1), V ₂(x _V2, y _V2, z _V2), the angle of two normal vectors is α, i.e. angle between two tri patchs, and the formula of calculating is:

$\mathrm{\&alpha;}=\arccos \frac{x_{v1}*x_{v2}+y_{v1}*y_{v2}+z_{v1}*z_{v2}}{\sqrt{{x_{v1}}^2+{y_{v1}}^2+{z_{v1}}^2}\sqrt{{x_{v2}}^2+{y_{v2}}^2+{z_{v2}}^2}}$

The angle α between the geological interface then ^*Expression formula be:

Wherein n equals the angle number of the tri patch of two geological interfaces in same block unit.

Geological interface three-dimensional configuration analytical approach based on TIN according to claim 1 is characterized in that the computing method of distance field are:

Certain puts the distance dependent of the geological interface that is associated in control geologic agent field, ore deposit and the space, and promptly controlling geologic agent field, ore deposit is certain spatially distributed functions of putting the geological interface distance in the space,

Obtaining the prediction space is the distance value of each unit correspondence in the aforesaid study area geological space, sets up the distance field model, the minimum value of the central point that described distance value refers to some unit distance value of each tri patch in the TIN model.

Form trend and form fluctuating that grading extraction goes out geological interface comprise:

What the space trend model reflected is the body feature of space object on area of space, and it has been ignored local form and has risen and fallen to disclose the body feature on the area of space.In the geology of mineral deposit space, the subject form of plastid will play the influence of certain factor to becoming the ore deposit on every side relatively, and rising and falling then is the side reflection of geologic anomaly effect.Therefore, the analysis of plastide morphology will be the important step of control ore deposit factor dose over the ground.

The form trend of described geological interface is meant the new TIN model that new summit that the Z value on the summit of the tri patch in the geological interface TIN model is obtained according to square distance inverse ratio method assignment is again set up, new TIN model is called the trend surface of geological interface, and the forming process of the trend surface of geological interface is as follows:

1. determine detection range d, have only with the sample spot of estimation point distance could participate in calculating that its middle distance is meant at 2 in the distance between subpoint on the XY plane, rather than 2 absolute distance less than d; The estimation point refers to the subpoint of any one summit on the XY plane in the original geological interface TIN model;

2. utilize square distance inverse ratio method to recomputate all z values of sample spot, formula is as follows:

$z=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{z_i}{d_i^2}}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{1}{d_i^2}}$

Wherein, z _iRepresent around this estimation point, with the vertical coordinate component of estimation point distance less than the sample spot of d; d _iThe distance of representing this estimation point and sample spot; Distance all refers at 2 in the distance between subpoint on the XY plane herein;

3. utilize the z value of calculating, set up new geological interface TIN model, form the trend surface of geological interface;

According to the method described above, adopt different detection range d, get final product the form trend that grading extraction obtains geological interface;

Described form rises and falls and is meant the relief intensity of geological interface with respect to the form trend surface, and promptly the z value in the geological interface deducts the z value of form trend surface, can obtain form and rise and fall.

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