{deduct} max air shoes -_Ray Tracing in C# and .NE

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Ray Tracing in C# and .NET
Source code: Raytracing.zip 104 KB I just saw the Japanese Animation film Spirited Away and couldn;t aid admiring the fusion of cool moving graphics, microcomputer generated backgrounds, and integration of sound. This inspired me apt revisit the globe of 3-D microcomputer graphics. One of the coolest techniques in generating 3-D objects namely known for ray tracing. This technique utilizes how the action of a mote of light (a photon) with a solid alternatively refractive thing. We are merely amused in the rays namely reflect into the camera alternatively view district close the eye. This “view” place forms the image from the another colors and intensities bouncing back from the solid thing.Sounds extra like a science project than a microprocessor procedure, merely the ray tracing algorithm namely pure numbers (geometry and algebra). The sphere is the simplest object apt ray trace, for the sphere tin be described in one uncomplicated formula, where additional fashions such for a cube need to be described for the combination of several planes. The formula for the sphere is:(xs– xc)2 + (ys – yc)2 + (zs– zc)2 – rs2 = 0where:xs is the xcoordinate of a point aboard the spherexcis the x coordinate of the centre of the spherers is the radius of the sphereThe majority of calculation in Ray Tracing is in discovery a method to test because the crossing point of the object you are viewing. By the direction, we are not cared with speed in this procedure. If we were concerned with speed, we would use a watered-down edition of ray tracing known as ray casting which is the technique accustomed to manner the graphics you see in Doom, Quake, Duke Nukem and other animation software that requires quick performance. The elementary equation for a ray (or line) in 3D space is shown below: R(t)= Ro + Rd * t ( t > 0)where: Ro is the origin point of the ray by (xo, yo, zo)Rd is the instruction of the ray at (xd, yd, zd) and is a element vector (xd2 + yd2 + zd2 = 1)rs is the radius of the sphereYou can almost consider of it as the formula of a line in 3d space where Ro is the y intercept and Rd is the tilt. Now let;s see at a use circumstance of the ray tracing algorithmFor every pixel ashore the surface of a 2-D shade namely the eye or camera is viewing, determine the world coordinates of the pixel.Cast a ray from the “camera” through the pixelCheck for an intersection with a solid object (in this case a sphere.)For the nearest intersection with the solid object, determine a screen corresponding to the distance of the ray to the object.Let;s look at the math in the algorithm and take a look at the Ray tracing formula broken up into its Cartesian coordinates:x(t) = xo + xd * t (t > 0) y(t) = yo + yd* t z(t) = zo + zd* t If we immediately substitute the ray formula into the equation for a sphere we get: (xo + xd * t – xc)2 + (yo + yd * t – yc)2 + (zo + zd* t – zc)2 – rs2 = 0This formula can be solved for t by using the quadratic equation where: A = xd2+ yd2 + zd2 = 1 (because it;sa element vector) B = 2 [xd(xo -xc) + yd(yo -yc) + zd(zo -zc) ]C = (xo -xc) 2 + (yo -yc) 2+ (zo -zc) 2 So by the quadratic formula : tintersect= -B +/- Sqrt ( B2 – 4C)/2 The discriminant B2 – 4C must be greater than naught or there is no intersection (B2 – 4C Now we have everything we need to determine the point of intersection and then the Normal vector. The normal vector is the vector vertical to the ray of intersection. We need this to obtain our last pixel. The point of intersection is the solution that we came up for t plugged behind into the vector: (xi,yi, zi,) = (xo + xd *tintersect, yo + yd * tintersect,zo + zd * tintersect)The natural vector at the point of intersection is determinedfrom the formula below: (xn,yn, zn,) = (xi – xc)/rs, (yi –y c)/r s, (zi –zc)/r s,Let;s bring an end to ... the mathematical use case for calculating the pixels in the view another tab-stops:list .5in">1) Calculate the coefficients A,Air Max 90 shoes, B and C from the quadratic solution using the direction vector of the ray, the ray origin point, the center point of the sphere, and the radius of the sphere.tab-stops:list .5in">2) Use A, B,chi hair dryers, and C to enumerate the point where the ray intersects with the sphere.tab-stops:list .5in">3) If the discriminant B2 – 4C is less than 0, the ray does not intersecttab-stops:list .5in">4) If one of the roots of the solution t = -B +/- Sqrt ( B2 – 4C)/2 has a basis where ttab-stops:list .5in">5) We want all solutions where t >= 0 but is the smaller of the two roots.tab-stops:list .5in">6) Use t to think the intersection pointtab-stops:list .5in">7) Use the intersection point to count the normal vectorOnce we determine whether the ray intersects with the object, we need to determine the shading of the pixel based on the vector of a light source. The shading of the pixel is decisive by the internal product of the light source vector with the normal vector ray intersecting the object and anyone ambient light.Shading = | Rn* La + ambient |Now we have everything we need to build our ray-traced sphere in software. Below is the UML design of our ray tracing C# program divided into the kernel objects Shape, Vector, normal">Light, LightIntensity, Color, normal">Camera, View2D. The objects Sphere and normal">Plane are objects for viewing that inherit from the Shape object and override the DoesRayIntersect method. normal">Light and LightIntensity classes are used to determine the shading of the object based on the formula upon. The View2D level is used to paint the pixel from the intersecting ray and the color determined from the Shading formula to the Form. The Camera class is used to determine every example ray being passed to the algorithm. Most of the algorithm occurs in the overridden normal">DoesRayIntersect method of the another shapes which not only determines if the ray sample intersects the object, but returns where it intersects if it does.Click Here for Figure 2UML Diagram of Ray Tracing Algorithm, reverse engineered using theWithClass UML ToolThe DoesRayIntersect method of the sphere used to determine the intersection of the ray with the sphere is shown under. This method is shrieked in the Form;s Paint Event Handler for each pixel in the normalized camera grid to test and find the intersection of the ray from the camera to the sphere object and draws it if it exists. Note how DoesRayIntersect steps through each tread of the algorithm and checks t according the access to determine its a valid ray intersecting with the sphere.public override bool DoesRayIntersect(Vector Ro, Vector Rd, ref Vector v){// Determine initial situation (Ro – Rc) = (origin of ray – sphere center) Vector vec = Ro – Rc; // Use Rd and vec to determine the b component of the quadratic for // the determinant by catching the dot production double b = Rd * vec;// calculate the c makeup of the quadratic from (Ro-Rc)^2 – (radius of sphere) double c = vec * vec – radius * radius; // calculate the discriminant double discriminant= b * b – c;// if the discriminant if (discriminant// calculate t for the ray double dsquared = Math.Sqrt(discriminant);double t = -b + dsquared ;// if t is less than naught, the ray is coming from inside the sphere, skip it. // We only ambition the smallest basis, t, that is assured. if(t // t meets always the necessary conditions. // calculate the intersecting vector by substituting t back in Vector v1 = Rd * t + Ro; v1 = v1 – Rc;// normalize the vector(scale the vector such that x^2 + y^2 + z^2 = 1)v1.normalize();v = v1;return true;}After the intersection is decisive and the normal vector is calculated, we can join the vector with the lighting vector to get a color for the vector. This is done with our LightIntensity object in the DetermineIntensity method shown below: public void DetermineIntensity(Vector rayVector, ref Color aColor)// take the dot production of the light source vector and the vector we just determined // multiplication the ambient merit // use the ruddy color for shadingaColor.red = (lightSource.V * rayVector) + ambientLight; if (aColor.red We can too paint the 3D vector on a 2D surface using the x and y coordinates of the ray with the help of the DrawPixel method in the View2D class. We;ll use the resolution of the surface to scale the vector up so we can watch it on the form. Also memorandum that we add one to the position to make sure its not sitting in the negate plane of the fashion. A pen is created using the color we just came up with in our LightIntensity Object. publicvoid DrawPixel(Color color, Graphics g, Vector position)// scale up the vector x and y coordinates so we can penetrate them on the form. // Also translate them into the assured plane.integer x = (int) ((position.x+ 1.0) * (resolutionX/5)); int y = (int)((position.y+ 1.0) * (resolutionY/5)); //Draw a pixel according to the color that we determined from our LightIntensity class. Convert our Color class // to the inner .NET color class using the Argb feature g.DrawLine(fashionable Pen(System.Drawing.Color.FromArgb(color.GetRed(), (int)color.GetGreen(),(int)color.GetBlue()), 1), (int)x,(int)y,chi hair iron, (int)x+1, (int)y);}Drawing a Plane Although we didn;t talk approximately them in this article, the code likewise contains ray tracing for planes as well. If you want to analyze ray tracing of planes, you can attempt uncommenting the code in the Form for creating a plane and remark out the code for drawing a sphere. The algorithm for drawing a plane is slightly alter, though we derive t through the same algebraic method we did for the sphere. Some of the references below will give you a nice mind on how a plane is ray-traced.References on the Web This treatise was amplified referencing the message from the emulating links: Ray Tracing by SigGraphRay Tracing: Graphics for the massesConclusionRay tracing is a very powerful demonstration of what a computer is capable of graphically purely through mathematics. With other techniques such as refraction and texture mapping you can produce some beautiful awesome spectacles on your computer shade. Have amusement tracing your steps in .NET!The Complete Visual C# Programmer;s Guide covers most of the major components that make up C# and the .NET environment. The writing is geared toward the intermediate programmer, but contains enough matter to satisfy the perfected developer. The writing starts by introducing the reader to the .NET surroundings and some basic C# program instances. The book then works in depth on how to voyage the Visual Studio environment and introduces the reader to the C# language From here the book swoops into the .NET framework and how to take vantage of its capabilities using C#. Some of the topics covered in large detail comprise ADO.NET database programming, ASP.NET and Web Services, COM interoperability programming, security in .NET, mobile call programming, GDI+ graphic programming, multithreading,discount max air shoes, Windows Services,farouk chi flat iron, XML and SOAP in .NET, and many more. Chapters in the book involve programming instances, reference charts, and step-by-step tutorials to adviser you through one of Microsoft;s greatest completions in programming environments.Mike Gold is President of Microgold Software Inc. and Creator of WithClass 2000 a UML Design Tool for C#. Visit http://www.microgold.com/. In the last few years Mike has consulted for companies such as Merrill Lynch and Chase Manhattan Bank in New York. He is been vigorous in developing Visual C++ Applications for 10 years and looks amenable to the possibilities in C#. You can approach him at techsupport@microgold.com.