CN104180269A - Automobile headlamp optical system - Google Patents

Abstract

The invention provides an automobile headlamp optical system which comprises an LED light source, a reflection part and a lens. The reflection part comprises a first reflecting mirror, a reflecting plate, a baffle and a second reflecting mirror. The first reflecting mirror comprises a first main reflecting mirror body and a first auxiliary reflecting mirror body. The portion, on the rear of the baffle, of the reflecting plate is used for reflecting some light shielded by the baffle to the lens secondarily so that a dipped headlight light type with light and shade cut-off lines can be obtained. The first reflecting mirror is shaped like an ellipsoid. The LED light source and an optical axis are vertically arranged on a first focal point of the ellipsoid. The first reflecting mirror is the upper half portion of the ellipsoid and extends to a second focal point. The baffle is arranged on the portion, located on the second focal point of the first reflecting mirror, of the ellipsoid. The portion, on the top of the baffle, of the reflecting plate reflects some light shielded by the baffle to the lens secondarily so that a dipped headlight light type with light and shade cut-off lines can be obtained; meanwhile, most of the light shielded and filtered out is fully utilized, and the utilization rate of luminous flux is increased.

Description

A kind of vehicle front lighting lamp optical system

Technical field

The present invention relates to LED lighting field, especially a kind of vehicle front lighting lamp optical system.

Background technology

Existing LED automobile short-distance headlamp is used projector structure mostly, a kind of vehicle front lighting dipped headlights as disclosed in Chinese utility model patent (CN201561349U), its luminescence unit and radiator are superimposed, each luminescence unit is comprised of reflector 7, baffle plate 5, lens 2 and light source 10, its operation principle is: the light that reflector 7 sends LED light source 10 converges, through baffle plate 5, shelter from part light to form "cut-off"line, light obtains having the dipped beam type of "cut-off"line again after lens 2 converge; The shortcoming that this lower beam headlamp exists mainly contains: 1. light is by baffle plate 5 eclipsing losses, and the utilization rate of the light that LED light source 10 sends is lower, and the utilization rate of luminous flux of light source is lower; 2. the light that the reflecting surface of reflector 7 far-ends reflects, reflex to which direction and reflect emitted light angle all more than 12 ° through lens 2, and this part light is mapped to apart from light fixture 3.5m with interior scope apart from ground level 0.75m calculating (0.75/tan12 °=3.5) recent photograph by light fixture, and this part light in driving without any meaning, so this part light also belongs to waste.Therefore the irradiation distance of the light of this lower beam headlamp is near, light width is narrower, light light is darker.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of vehicle front lighting lamp optical system, meets under the prerequisite of car headlamp related request, and distance that light irradiates is farther, width increases, brightness is higher.

For solving the problems of the technologies described above, technical scheme of the present invention is: a kind of vehicle front lighting lamp optical system, comprise LED light source, reflecting part and lens, described reflecting part comprise be positioned at LED light source top the first speculum, be positioned at the first speculum below reflecting plate, be positioned at the baffle plate in reflecting plate the place ahead and be positioned at the second speculum of below before baffle plate; Described the first speculum comprises LED light source light is converged and reflexes to the first principal reflection mirror of lens and LED light source light is converged to the first auxiliary speculum that reflexes to the second speculum and then reflex to lens; Reflecting plate by baffle plate rear secondary reflects to lens the part light being blocked by baffle plate, to obtain having the dipped beam type of "cut-off"line;

Described the first speculum is elliposoidal, and described LED light source is arranged on the first focus place of ellipsoid in the mode vertical with optical axis, and described the first speculum is elliposoidal the first half and by the second focus place;

Described baffle plate is arranged on the second focus place of elliposoidal the first speculum, and described baffle plate left side is the straight line of level, right side be the oblique line at 45 ° that makes progress to horizontal line vertically apart from the broken line of 25cm steering horizontal.

The present invention secondary reflects to lens by the reflecting plate at baffle plate top the part light being blocked by baffle plate, to obtain having the dipped beam type of "cut-off"line, the most of light filtering that is simultaneously blocked is fully used, the utilization rate of luminous flux is improved, and light distribution effect is significantly promoted, the irradiation distance of light, width are obviously increased; By the first auxiliary speculum and the second speculum, coordinated the light of speculum front end is secondary reflected to the place ahead, lens bottom, the light luminance of enhancing light also forms the illumination in III district.

As improvement, the free curve design method of described lens:

The light type of automobile dipped headlight can be divided into first area, four regions, second area, the 3rd region, the 4th region, there is corresponding illumination requirement value in each region, the 3rd region is glare area, its maximal illumination can not surpass 0.7lux, when design free-form surface lens, the light sending from ellipsoid the second focus is divided into three parts according to angle and projects respectively the 3rd extra-regional other three regions of removing photometric screen, so just can form specific distribution of light situation;

After dividing through region, according to law of conservation of energy, can set up the energy and the relational equation that is irradiated to the energy of photometric screen after ellipsoid the first speculum:

If given light is distributed as P ₀, the central light strength of light source is I ₀, consideration direction is θ ₁the position of the photometric screen that incides of light be r ₁, be less than θ with axis angle ₁the position coordinates of light incident be also less than r ₁, by the light θ of first ₁be divided into i part, corresponding each θ ₁in radius r ₁on be all divided into i part, so just obtained array θ ₁and r (i) ₁(i), the conservation of energy expression formula of the illumination on first area emergent light and screen is so:

$2\mathrm{\π}{\∫}_0^{{\mathrm{\θ}}_1\left(i\right)}{I}_0\cos \mathrm{\θ}\sin \mathrm{\θ}\·\mathrm{d\θ}=2\mathrm{\π}{\∫}_0^{r_1\left(i\right)}{P}_0\·r\·\mathrm{dr}---\left(4\right)$

Angle is θ ₁～θ ₂between the light position of inciding photometric screen be r ₁～r ₂, this part light is divided into j part, corresponding each angle has been divided into j part on radius, and the conservation of energy expression formula of the illumination on emergent light and screen is:

$2\mathrm{\π}{\∫}_{{\mathrm{\θ}}_1}^{{\mathrm{\θ}}_2\left(j\right)}{I}_0\cos \mathrm{\θ}\sin \mathrm{\θ}\·\mathrm{d\θ}=2\mathrm{\π}{\∫}_{r_1}^{r_2\left(j\right)}{P}_0\·r\·\mathrm{dr}---\left(5\right)$

In like manner, can obtain the 3rd region energy conservation expression formula is:

$2\mathrm{\π}{\∫}_{{\mathrm{\θ}}_2}^{{\mathrm{\θ}}_3\left(k\right)}{I}_0\cos \mathrm{\θ}\sin \mathrm{\θ}\·\mathrm{d\θ}=2\mathrm{\π}{\∫}_{r_2}^{r_3\left(k\right)}{P}_0\·r\·\mathrm{dr}---\left(6\right)$

By these three expression formulas, the relational expression that can obtain respectively between each zone radius and emergent light angle is as follows:

$r_1\left(i\right)=\sqrt{\frac{I_0}{P_0}\·{\sin }^2{\mathrm{\θ}}_1\left(i\right)}---\left(7\right)$

$r_2\left(j\right)=\sqrt{\frac{I_0}{P_0}\·({\sin }^2{\mathrm{\θ}}_2\left(j\right)-{\sin }^2{\mathrm{\θ}}_1)+{r_1}^2}---\left(8\right)$

$r_3\left(k\right)=\sqrt{\frac{I_0}{P_0}\·({\sin }^2{\mathrm{\θ}}_3\left(k\right)-{\sin }^2{\mathrm{\θ}}_2)+{r_2}^2}---\left(9\right)$

According to the characteristic of ellipsoid the first speculum, light source position is when first speculum the first focus, light penetrates the second focus from the first speculum, thereby the light of the second focus outgoing can be regarded as to a spot light outgoing, the second focus of ellipsoid the first speculum of take is set up coordinate system as initial point, and the rear cut-off distance f=15mm of lens is set, free-form surface lens has two faces, first surface is a cylinder, and second is free form surface, in the first surface application law of refraction:

$\frac{\sin \mathrm{\θ}}{{\sin \mathrm{\θ}}^{\′}}=\frac{n^{\′}}{n}---\left(10\right)$

Light incides free form surface medium from air, the refractive index of air is n=1, and free-form surface lens is used material PC to make, refractive index n=1.591, first fold exit point A point coordinates value can be tried to achieve as (ftan (θ), f), and the slope value of refracted ray AB is cot (θ '), utilizes point slope form can obtain the linear equation of AB;

Light reflects when through second of free-form surface lens, and the vector form of the law of refraction can be expressed as:

${[1+n^2-2n(\stackrel{\→}{\mathrm{Out}}\·\stackrel{\→}{\mathrm{In}})]}^{1/2}\·\stackrel{\→}{N}=\stackrel{\→}{\mathrm{Out}}-n\·\stackrel{\→}{\mathrm{In}}---\left(11\right)$

Wherein: n is free form surface medium refraction index, for incident ray unit vector, for emergent ray unit vector, for the unit normal vector of free form surface at light incidence point; When calculating second face type, first determine the initial point of a calculating, if the some B coordinate that light incides on free form surface after first surface refraction is (x, z), the point C coordinate that light projects on screen after lens reflection is (r, H), H=25m wherein, r is determined by formula (7), (8), (9) according to law of conservation of energy; So, the unit vector of incident ray AB and emergent ray BC all can be tried to achieve, recycling law of refraction formula (11) can obtain the normal vector that B is ordered, thereby determine the section of this point, thereby this section and more lower the more lower of the definite free form surface of ray intersection on free form surface that incide after first surface refraction; By the straight line at more front section and more lower normal vector place, intersect and obtain down a bit, by computer iterations, can obtain the coordinate of each point, thereby determine the coordinate of each point on free form surface.

The beneficial effect that the present invention compared with prior art brought is:

The present invention secondary reflects to lens by the reflecting plate at baffle plate top the part light being blocked by baffle plate, to obtain having the dipped beam type of "cut-off"line, the most of light filtering that is simultaneously blocked is fully used, the utilization rate of luminous flux is improved, and light distribution effect is significantly promoted, the irradiation distance of light, width are obviously increased; By the first auxiliary speculum and the second speculum, coordinated the light of speculum front end is secondary reflected to the place ahead, lens bottom, the light luminance of enhancing light also forms the illumination in III district.

Accompanying drawing explanation

Fig. 1 is structural representation of the present invention.

Fig. 2 is decomposition view of the present invention.

Fig. 3 is cross-sectional view of the present invention.

Fig. 4 is distribution of light figure.

Fig. 5 is free-form surface lens design diagram.

The specific embodiment

Below in conjunction with Figure of description, the invention will be further described.

As shown in Figures 1 to 3, a kind of vehicle front lighting lamp optical system, comprise LED light source 5, reflecting part and lens 3, described reflecting part comprise be positioned at LED light source 5 tops the first speculum 1, be positioned at the first speculum 1 below reflecting plate 4, be positioned at the baffle plate 2 in reflecting plate 4 the place aheads and be positioned at baffle plate 2 the second speculum 6 of below above; Described the first speculum 1 comprises LED light source 5 light is converged and reflex to the first principal reflection mirror 11 of lens 3 and LED light source 5 light are converged to the first auxiliary speculum 12 that reflexes to the second speculum 6 and then reflex to lens 3; Reflecting plate 4 by baffle plate 2 rears secondary reflects to lens 3 the part light being blocked by baffle plate 2, to obtain having the dipped beam type of "cut-off"line.

Described the first speculum 1 is elliposoidal, and oval equation is:

$\frac{z^2}{a^2}+\frac{y^2}{b^2}=1---\left(1\right)$

a ²-b ²＝c ² (2)

-a≤z≤c,y≥0 (3)

In formula, a and b are oval long and short semiaxis, c be focus to the distance of the origin of coordinates, by this elliptic curve along bus Rotate 180 °.Ellipsoid has two focuses, LED light source is placed on to the first focus place of ellipsoid in the mode vertical with optical axis, and the light that light source sends is assembled at the second focus place after reflection.Because the approximate lambert's body of LED light source is luminous, thus 1 need of ellipsoid the first speculum are got the first half and by it by the second focus place.

According to international standard requirement, on the photometric screen of 25 meters, dipped beam should produce obvious "cut-off"line, and its horizontal component is positioned at v-v line left side, right side be with horizontal alignment on the oblique line of 15 °, or the oblique line at 45 ° that makes progress to horizontal line vertically apart from the broken line of 25cm steering horizontal.In order to form "cut-off"line clearly, baffle plate 2 should be placed on to the second focus place of ellipsoid the first speculum 1.The straight line that the design's baffle plate 2 left sides are level, right side be the oblique line at 45 ° that makes progress to horizontal line vertically apart from the broken line of 25cm steering horizontal, and design with base integrated.

The free curve design method of described lens 3:

The light type of automobile dipped headlight can be divided into first area, four regions, second area, the 3rd region, the 4th region, there is corresponding illumination requirement value in each region, the 3rd region is glare area, its maximal illumination can not surpass 0.7lux, when design free-form surface lens 3, the light sending from ellipsoid the second focus is divided into three parts according to angle and projects respectively the 3rd extra-regional other three regions of removing photometric screen, as shown in Figure 4, so just can form specific distribution of light situation, wherein O point is ellipsoid the second focus.

After dividing through region, according to law of conservation of energy, can set up the energy and the relational equation that is irradiated to the energy of photometric screen after ellipsoid the first speculum 1:

If given light is distributed as P ₀, the central light strength of light source is I ₀, consideration direction is θ ₁the position of the photometric screen that incides of light be r ₁, be less than θ with axis angle ₁the position coordinates of light incident be also less than r ₁, by the light θ of first ₁be divided into i part, corresponding each θ ₁in radius r ₁on be all divided into i part, so just obtained array θ ₁and r (i) ₁(i), the conservation of energy expression formula of the illumination on first area emergent light and screen is so:

$2\mathrm{\π}{\∫}_0^{{\mathrm{\θ}}_1\left(i\right)}{I}_0\cos \mathrm{\θ}\sin \mathrm{\θ}\·\mathrm{d\θ}=2\mathrm{\π}{\∫}_0^{r_1\left(i\right)}{P}_0\·r\·\mathrm{dr}---\left(4\right)$

Angle is θ ₁～θ ₂between the light position of inciding photometric screen be r ₁～r ₂, this part light is divided into j part, corresponding each angle has been divided into j part on radius, and the conservation of energy expression formula of the illumination on emergent light and screen is:

$2\mathrm{\π}{\∫}_{{\mathrm{\θ}}_1}^{{\mathrm{\θ}}_2\left(j\right)}{I}_0\cos \mathrm{\θ}\sin \mathrm{\θ}\·\mathrm{d\θ}=2\mathrm{\π}{\∫}_{r_1}^{r_2\left(j\right)}{P}_0\·r\·\mathrm{dr}---\left(5\right)$

In like manner, can obtain the 3rd region energy conservation expression formula is:

$2\mathrm{\π}{\∫}_{{\mathrm{\θ}}_2}^{{\mathrm{\θ}}_3\left(k\right)}{I}_0\cos \mathrm{\θ}\sin \mathrm{\θ}\·\mathrm{d\θ}=2\mathrm{\π}{\∫}_{r_2}^{r_3\left(k\right)}{P}_0\·r\·\mathrm{dr}---\left(6\right)$

By these three expression formulas, the relational expression that can obtain respectively between each zone radius and emergent light angle is as follows:

$r_1\left(i\right)=\sqrt{\frac{I_0}{P_0}\·{\sin }^2{\mathrm{\θ}}_1\left(i\right)}---\left(7\right)$

$r_2\left(j\right)=\sqrt{\frac{I_0}{P_0}\·({\sin }^2{\mathrm{\θ}}_2\left(j\right)-{\sin }^2{\mathrm{\θ}}_1)+{r_1}^2}---\left(8\right)$

$r_3\left(k\right)=\sqrt{\frac{I_0}{P_0}\·({\sin }^2{\mathrm{\θ}}_3\left(k\right)-{\sin }^2{\mathrm{\θ}}_2)+{r_2}^2}---\left(9\right)$

According to the characteristic of ellipsoid the first speculum 1, light source position is when first speculum 1 the first focus, and light penetrates the second focus from the first speculum 1, thereby the light of the second focus outgoing can be regarded as to a spot light outgoing; As shown in Figure 5, the second focus of ellipsoid the first speculum 1 of take is set up coordinate system as initial point, and the rear cut-off distance f=15mm of lens 3 is set, and free-form surface lens 3 has two faces, and first surface is a cylinder, and second is free form surface, in the first surface application law of refraction:

$\frac{\sin \mathrm{\θ}}{{\sin \mathrm{\θ}}^{\′}}=\frac{n^{\′}}{n}---\left(10\right)$

Light incides free form surface medium from air, the refractive index of air is n=1, and free-form surface lens 3 is used material PC to make, refractive index n=1.591, first fold exit point A point coordinates value can be tried to achieve as (ftan (θ), f), and the slope value of refracted ray AB is cot (θ '), utilizes point slope form can obtain the linear equation of AB;

Light reflects when through 3 second of free-form surface lens, and the vector form of the law of refraction can be expressed as:

${[1+n^2-2n(\stackrel{\→}{\mathrm{Out}}\·\stackrel{\→}{\mathrm{In}})]}^{1/2}\·\stackrel{\→}{N}=\stackrel{\→}{\mathrm{Out}}-n\·\stackrel{\→}{\mathrm{In}}---\left(11\right)$

Wherein: n is free form surface medium refraction index, for incident ray unit vector, for emergent ray unit vector, for the unit normal vector of free form surface at light incidence point; When calculating second face type, first determine the initial point of a calculating, if the some B coordinate that light incides on free form surface after first surface refraction is (x, z), the point C coordinate that light projects on screen after lens 3 refractions is (r, H), H=25m wherein, r is determined by formula (7), (8), (9) according to law of conservation of energy; So, the unit vector of incident ray AB and emergent ray BC all can be tried to achieve, recycling law of refraction formula (11) can obtain the normal vector that B is ordered, thereby determine the section of this point, thereby this section and more lower the more lower of the definite free form surface of ray intersection on free form surface that incide after first surface refraction; By the straight line at more front section and more lower normal vector place, intersect and obtain down a bit, by computer iterations, can obtain the coordinate of each point, thereby determine the coordinate of each point on free form surface.

Claims (2)

1. a vehicle front lighting lamp optical system, comprise LED light source, reflecting part and lens, it is characterized in that: described reflecting part comprise be positioned at LED light source top the first speculum, be positioned at the first speculum below reflecting plate, be positioned at the baffle plate in reflecting plate the place ahead and be positioned at the second speculum of below before baffle plate; Described the first speculum comprises LED light source light is converged and reflexes to the first principal reflection mirror of lens and LED light source light is converged to the first auxiliary speculum that reflexes to the second speculum and then reflex to lens; Reflecting plate by baffle plate rear secondary reflects to lens the part light being blocked by baffle plate, to obtain having the dipped beam type of "cut-off"line;

Described the first speculum is elliposoidal, and described LED light source is arranged on the first focus place of ellipsoid in the mode vertical with optical axis, and described the first speculum is elliposoidal the first half and by the second focus place;

Described baffle plate is arranged on the second focus place of elliposoidal the first speculum, and described baffle plate left side is the straight line of level, right side be the oblique line at 45 ° that makes progress to horizontal line vertically apart from the broken line of 25cm steering horizontal.

2. a kind of vehicle front lighting lamp optical system according to claim 1, is characterized in that: the free curve design method of described lens:

The light type of automobile dipped headlight can be divided into first area, four regions, second area, the 3rd region, the 4th region, there is corresponding illumination requirement value in each region, the 3rd region is glare area, its maximal illumination can not surpass 0.7lux, when design free-form surface lens, the light sending from ellipsoid the second focus is divided into three parts according to angle and projects respectively the 3rd extra-regional other three regions of removing photometric screen, so just can form specific distribution of light situation;

After dividing through region, according to law of conservation of energy, can set up the energy and the relational equation that is irradiated to the energy of photometric screen after ellipsoid the first speculum:

If given light is distributed as P ₀, the central light strength of light source is I ₀, consideration direction is θ ₁the position of the photometric screen that incides of light be r ₁, be less than θ with axis angle ₁the position coordinates of light incident be also less than r ₁, by the light θ of first ₁be divided into i part, corresponding each θ ₁in radius r ₁on be all divided into i part, so just obtained array θ ₁and r (i) ₁(i), the conservation of energy expression formula of the illumination on first area emergent light and screen is so:

$2\mathrm{\π}{\∫}_0^{{\mathrm{\θ}}_1\left(i\right)}{I}_0\cos \mathrm{\θ}\sin \mathrm{\θ}\·\mathrm{d\θ}=2\mathrm{\π}{\∫}_0^{r_1\left(i\right)}{P}_0\·r\·\mathrm{dr}---\left(4\right)$

Angle is θ ₁～θ ₂between the light position of inciding photometric screen be r ₁～r ₂, this part light is divided into j part, corresponding each angle has been divided into j part on radius, and the conservation of energy expression formula of the illumination on emergent light and screen is:

$2\mathrm{\π}{\∫}_{{\mathrm{\θ}}_1}^{{\mathrm{\θ}}_2\left(j\right)}{I}_0\cos \mathrm{\θ}\sin \mathrm{\θ}\·\mathrm{d\θ}=2\mathrm{\π}{\∫}_{r_1}^{r_2\left(j\right)}{P}_0\·r\·\mathrm{dr}---\left(5\right)$

In like manner, can obtain the 3rd region energy conservation expression formula is:

$2\mathrm{\π}{\∫}_{{\mathrm{\θ}}_2}^{{\mathrm{\θ}}_3\left(k\right)}{I}_0\cos \mathrm{\θ}\sin \mathrm{\θ}\·\mathrm{d\θ}=2\mathrm{\π}{\∫}_{r_2}^{r_3\left(k\right)}{P}_0\·r\·\mathrm{dr}---\left(6\right)$

By these three expression formulas, the relational expression that can obtain respectively between each zone radius and emergent light angle is as follows:

$r_1\left(i\right)=\sqrt{\frac{I_0}{P_0}\·{\sin }^2{\mathrm{\θ}}_1\left(i\right)}---\left(7\right)$

$r_2\left(j\right)=\sqrt{\frac{I_0}{P_0}\·({\sin }^2{\mathrm{\θ}}_2\left(j\right)-{\sin }^2{\mathrm{\θ}}_1)+{r_1}^2}---\left(8\right)$

$r_3\left(k\right)=\sqrt{\frac{I_0}{P_0}\·({\sin }^2{\mathrm{\θ}}_3\left(k\right)-{\sin }^2{\mathrm{\θ}}_2)+{r_2}^2}---\left(9\right)$

According to the characteristic of ellipsoid the first speculum, light source position is when first speculum the first focus, light penetrates the second focus from the first speculum, thereby the light of the second focus outgoing can be regarded as to a spot light outgoing, the second focus of ellipsoid the first speculum of take is set up coordinate system as initial point, and the rear cut-off distance f=15mm of lens is set, free-form surface lens has two faces, first surface is a cylinder, and second is free form surface, in the first surface application law of refraction:

$\frac{\sin \mathrm{\θ}}{{\sin \mathrm{\θ}}^{\′}}=\frac{n^{\′}}{n}---\left(10\right)$

Light incides free form surface medium from air, the refractive index of air is n=1, and free-form surface lens is used material PC to make, refractive index n=1.591, first fold exit point A point coordinates value can be tried to achieve as (ftan (θ), f), and the slope value of refracted ray AB is cot (θ '), utilizes point slope form can obtain the linear equation of AB;

Light reflects when through second of free-form surface lens, and the vector form of the law of refraction can be expressed as:

${[1+n^2-2n(\stackrel{\→}{\mathrm{Out}}\·\stackrel{\→}{\mathrm{In}})]}^{1/2}\·\stackrel{\→}{N}=\stackrel{\→}{\mathrm{Out}}-n\·\stackrel{\→}{\mathrm{In}}---\left(11\right)$

Wherein: n is free form surface medium refraction index, for incident ray unit vector, for emergent ray unit vector, for the unit normal vector of free form surface at light incidence point; When calculating second face type, first determine the initial point of a calculating, if the some B coordinate that light incides on free form surface after first surface refraction is (x, z), the point C coordinate that light projects on screen after lens reflection is (r, H), H=25m wherein, r is determined by formula (7), (8), (9) according to law of conservation of energy; So, the unit vector of incident ray AB and emergent ray BC all can be tried to achieve, recycling law of refraction formula (11) can obtain the normal vector that B is ordered, thereby determine the section of this point, thereby this section and more lower the more lower of the definite free form surface of ray intersection on free form surface that incide after first surface refraction; By the straight line at more front section and more lower normal vector place, intersect and obtain down a bit, by computer iterations, can obtain the coordinate of each point, thereby determine the coordinate of each point on free form surface.