JP2617820B2 - Illuminance calculation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an illuminance calculation method for generating an image using an electronic computer under the condition that an object having both diffuse reflection characteristics and specular reflection characteristics is illuminated by a surface light source. is there.

[0002]

2. Description of the Related Art The reflection characteristics of a general object can be described separately as a diffuse reflection component and a specular reflection component. For the diffuse reflection component, a method of analytically calculating the reflection intensity when illuminated by a perfect diffuse light source is known, for example, by Echiro Nakamae,
(Institute of Electronics, Information and Communication Engineers), New Media Technology Series, Computer Graphics, 1st Edition, published on January 30, 1987, Ohmsha, pages 144 to 145, as described on pages 144-145. Light rays are calculated using a predetermined mathematical formula. As for the specular reflection component, the illuminance of an object having perfect specular reflection characteristics such as a mirror is calculated by approximating a surface light source with a set of point light sources by, for example, known sampling.

[0003]

However, since the specular reflection component cannot be determined analytically except for an object having perfect specular reflection characteristics, the surface light source is approximated by a set of point light sources by known sampling. In this method, there is a problem of a moire pattern due to sampling, that is, a problem of pseudo pattern generation caused by a synergistic effect of a sampling period and an original pattern of an object. Since a large number of sampling points are required, there is a disadvantage that the calculation time increases.

[0004] The present invention overcomes the disadvantages of the prior art,
It is an object of the present invention to provide an illuminance calculation method for analytically calculating a specular reflection component of illuminance by a surface light source without sampling the surface light source and approximating it as a set of point light sources.

[0005]

The light source is a polygonal perfect diffusion surface light source, and a reflection model whose specular reflectance is determined by the angle between the regular reflection direction of the line of sight and the light source direction is used. Polar coordinate transformation is performed with the gazing point as the origin and the specular reflection direction of the line of sight as the Z axis. A light source is projected onto a unit sphere (a sphere having a radius of 1 with the origin at the center), and this is defined as an integration area. The illuminance is calculated by dividing an integration region into triangles on a spherical surface using a point of z = 1 and then integrating to divide the illuminance.
An illuminance calculation method for calculating the illuminance on the surface of a three-dimensional object illuminated by a polygonal light source having a perfect diffusion surface, wherein the polygonal light source faces the surface of the three-dimensional object at a predetermined distance. And (1) the regular reflection of the vertex coordinates of the polygonal light source, the brightness of the surface of the object, the position of the viewpoint, and the regular reflection direction of the line-of-sight vector E in the line-of-sight direction. A parameter consisting of a direction vector Er and a specular reflection characteristic defined by an angle formed by the light source vector Lp in the polygonal light source direction is input to the computer;
(2) Polar coordinate conversion is performed with the gazing point P as the origin and the specular reflection direction as the Z axis. (3) The polygonal light source is projected on a unit spherical surface centered on the gazing point P at the origin. The divided area is divided into triangles on a spherical surface. (5) In the divided triangle areas, the intensity of light rays reflected in the direction of the line of sight is integrated to obtain the illuminance on the surface of the object. It is.

[0006]

A function in which the specular reflectance is determined by the angle between the specular reflection direction of the line of sight and the direction of the light source is used as a reflection model, and this function is rotationally symmetric. The integrand becomes a function only of the angle from the Z axis,
The simplification of the method enables the specular reflection intensity to be obtained analytically, thereby solving the problem associated with sampling.

[0007]

An embodiment of the present invention will be described with reference to the drawings.

FIG. 1 is an explanatory diagram of specular reflection. In FIG. 1, reference numeral 10 denotes a polygonal light source (completely diffused light source S), 11 denotes the direction of the surface of the light source, 12 denotes a direction connecting the polygonal light source and the gazing point P, and 13 denotes the distance between the polygonal light source and the gazing point P. , 14 are constants (I _O ) that give the intensity per unit area of the emitted light, 15 is the angle between the direction of the surface of the light source and the direction connecting the polygonal light source and the gazing point P, and 16 is the vertex of the light source , 20 is the surface of the three-dimensional object, 21 is the specular reflection direction, 22 is the polygonal light source direction, 23 is the surface direction of the surface of the object, 24 is the line of sight, 25 is the gazing point P, 26 is the viewpoint, 27 is the viewpoint The angle (θ) between the regular reflection direction and the polygonal light source direction.

The principle of the present invention will be described with reference to FIG.

The radiation characteristic of the perfect diffuse light source S is described by equation (1). Here, _Io is a constant that gives the intensity of the reflected light beam per unit area, and φ is the angle between the surface normal of the light source and the vector connecting the light source and the gazing point P.

[0011]

(Equation 1)

When the vertices of the light source are viewed from the table, Vi is clockwise.
(I = 1, m). The specular reflectance is calculated using the angle θ between the regular reflection direction Er in the viewpoint direction E and the light source direction Lp.
When represented by (θ), the intensity Is of the light ray that is reflected by P and reaches the viewpoint is given by Equation (2).

[0013]

(Equation 2)

Since integration is difficult in this state, polar coordinate conversion is performed so that P is the origin and Er is the Z axis. Next, as shown in FIG. 2, Vi is projected on a sphere having a radius of 1 around P (this is called a unit sphere) to obtain Wi.
The area surrounded by Wi is named Ω. Since dS is described by equation (3) by the polar coordinate transformation, equation (2) is replaced by equation (4).
Is replaced by

[0015]

(Equation 3)

[0016]

(Equation 4)

In order to simplify the integration, Ω is decomposed into a triangle WzWiWi + 1 on the unit sphere by using the intersection (point z = 1) Wz between the Z axis and the unit sphere. WzWiWi + 1 to Δ
i. Viewing the function Fi from the point P, Wz, Wi, Wi +
If 1 is defined as a sign function that is 1 when clockwise and -1 when counterclockwise, Ω can be described by equation (5).

[0018]

(Equation 5)

Therefore,

[0020]

(Equation 6)

However,

[0022]

(Equation 7)

Since the integrand in equation (7) is a function of only θ, equation (7) can be obtained by first integrating with θ and then integrating with φ. When direct integration with respect to φ cannot be performed, approximation is performed by a polynomial using a known method such as Fourier approximation or Chebyshev approximation.

Next, embodiments will be described in detail.

As an example of specular reflection as a function of the angle of the regular reflection direction 21 with Er, a normalized Phong model is used.

G (θ) in equation (7) is given by equation (8). Here, Rs is a constant from 0 to 1.

[0027]

(Equation 8)

In this case, equation (7) becomes equation (9).

[0029]

(Equation 9)

To further simplify equation (9), the coordinate system is rotated about the Z axis. As shown in FIG. 3, Wi and Wi
The great circle passing through +1 (the circle on the unit sphere centered on the origin) is Γ
A great circle passing through w, Wi and Wz is denoted by ΓA, and a great circle passing through Wi + 1 and Wz is denoted by ΓB. The points where ΓΑ and 交 intersect the xy plane are denoted by TΑ and TΒ, and the great circle passing through TΑ and TΒ is denoted by Γxy. The intersection of ΓW and Γxy is defined as Uy. An intersection of a unit sphere with a straight line passing through the point P and orthogonal to the vectors PWz and PUy is defined by Ux. Let R be the intersection of the planes Σ and ΓW defined by P, Wz, and Ux. The angle between PWz and PR is defined as α, and the angle between PUx and PTΑ, PTΒ is defined as βΑ, βΒ, respectively. Equation 9 allows algebraic integration with θ and is modified as in equation (10). Equation (10) can be integrated by polynomial approximation.

[0031]

(Equation 10)

FIG. 4 is a block diagram showing an apparatus according to an embodiment of the present invention.
Shown in The specular reflection direction in the line-of-sight direction is Z
Performs polar coordinate transformation with axes and gazing points as origins. The spherical projection unit 2 projects the polygonal surface light source onto a unit circle having a radius of 1 around the origin. The area of the light source projected by the integration area dividing unit 3 is divided into triangles on a spherical surface using points of z = 1. The integration unit 4 integrates each divided area to obtain a total. Parameter input 5 is the input parameters of the position of the viewpoint, the position of the gazing point, the vertex coordinates of the light source, and the reflection characteristics of the gazing point.
Output from intensity 6 of specular reflection.

The operation of this embodiment is shown in the flow chart of FIG. The symbols used in the following description are given in FIGS.

(Start) (Polar coordinate transformation) 1-1 Obtain unit vector E from gazing point P toward the viewpoint (FIG. 1) 1-2 Calculate specular reflection Er of E 1-3. Origin is P, Er is Z axis (Spherical projection) 2-1 The vertices of the surface light source are viewed clockwise as V1, V2,. . . Vm. m represents the number of vertices. 2-2 For each Vi, find the intersection of a unit circle (a circle with a radius of 1 around P) and a half-line from P to Vi,
Define as Wi (division of integration region) 3-1 Define the intersection of the unit circle and the Z axis (the point at z = 1 on the Z axis) as Wz 3-2 Define as Wm + 1 = Wi 3-3 From 3-3 For values of i up to m, Wz, Wi,
Find a triangle Δi on a spherical surface having Wi + 1 as a vertex. 3-4 Find a coefficient Fi for each Δi. Fi is defined as: Fi = 1: Wz, Wi, Wi + 1 are clockwise as viewed from P −1: Other.

(Execution of integration) 4-1 Is = 0; initialization of specular reflection intensity, i = 1; initialization of loop variable 4-2 Finding α, βA, βB of FIG. 3 for each Δi 4-3 Equation 10 is integrated. Let the obtained value be Isi. 4-4 Is = Is + Fi × Isi, i = i + 1 4-5 Return to 4-2 if i is m or less (output of result) 5-1 Output specular reflection intensity Is (end) )

[0036]

According to the first aspect of the present invention, the illuminance of an object having a general specular reflection characteristic irradiated by a surface light source can be obtained without sampling. The light source used daily is often a large surface light source. An object generally has both diffuse reflection characteristics and specular reflection characteristics. By combining the present invention with the conventional method of calculating the luminance of a perfect diffuse reflection object (Reference 1), it is possible to generate an image under general lighting and object conditions. The present invention has an effect that it is an effective means for generating a realistic image.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram of specular reflection.

FIG. 2 is an explanatory view of projection onto a unit spherical surface.

FIG. 3 is an explanatory diagram of integration in a triangular area.

FIG. 4 is a block diagram of an apparatus according to an embodiment of the present invention.

FIG. 5 is a flowchart of the operation of one embodiment of the present invention.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 Polar coordinate transformation part 2 Spherical projection part 3 Integration area division part 4 Integration execution part 5 Parameter input 6 Illuminance of specular reflection 10 Polygonal light source (completely diffused light source S) 11 Direction of the light source in the direction of the plane 12 Polygonal light source and gazing point P 13 The distance between the polygonal light source 10 and the gazing point P 14 A constant (I ₀ ) that gives the intensity per unit area of the radiated light ray 15 The direction 11 to the surface normal to the light source, the polygonal light source, and the gazing point P
Angle (φ) with the direction 12 connecting the light source 16 vertices (V _{1 to} V ₄ ) of the light source 20 the surface of the three-dimensional object 21 the regular reflection direction 22 the polygonal light source direction 23 the surface normal direction of the object surface 24 the line-of-sight direction 25 Gaze point P 26 View point 27 Angle (θ) between the regular reflection direction 21 and the polygonal light source direction 22

Claims (1)

(57) [Claims] 1. A polygonal light source having a perfect diffusion surface.
An illuminance calculation method for calculating the illuminance on the surface (20) of the three-dimensional object illuminated by (3), wherein the polygonal light source (10) is arranged at a predetermined distance (13) from the surface (20) of the three-dimensional object. (1) the vertex coordinates of the polygonal light source (10), the brightness of the surface (20) of the object, and the position of the viewpoint (26); The position of the fixation point P (25) and the regular reflection direction vector E in the regular reflection direction (21) of the line-of-sight vector E in the line-of-sight direction (24)
A parameter consisting of r and a specular reflection characteristic defined by an angle (27) formed by the light source vector Lp in the polygonal light source direction (22) is input to the computer, and (2) the gazing point P (2
5) With the origin as the origin, polar coordinate conversion is performed with the regular reflection direction (21) as the Z axis, and (3) the polygonal light source (10) is projected on a unit spherical surface centered on the point of interest P (25) at the origin. (4)
The projected area is divided into triangles on a spherical surface, and (5) the line of sight (2
An illuminance calculation method for calculating the illuminance on the surface of the object by integrating the intensity of the light source reflected in 4)