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errain ModelingWrite a graphics program using C/C++ and OpenGL to produce and display an interactive terrain mesh. Terrain meshes are models typically comprised of either triangle or quad polygons that make up a 3D surface. They are often used to represent outdoor virtual environments (e.g., fields, hills, mountains, etc.). An example terrain is shown to the right. For the purpose of your assignment, you will need to represent the terrain as a heightmap (a 2D array of height values), procedurally produce height values according to a specified algorithm, and display the resulting terrain using either triangle or quad (strip) primitives. See below for details on each point. When “make” is called, a program called Terrain.x should be compiled and generated. RepresentationAs discussed in class, terrains can be represented as a heightmap, a 2D array of height values. Then, every 2x2 sub-array of this heightmap represents the four corners of one quad (or the four corners of two triangles with a shared edge). If the height direction is represented by the y axis, then the x and z directions can be used as indices into the array for the y height value for each xz vertex. The size of the grid should be selectable by the user. Your program should support a terrain of sizes ranging from 50x50 to 300x300 vertices (you can also go higher if you want, but bear in mind the larger the terrain, the more computationally intensive it will be to render). Producing height valuesInitial height values should be generated using the so-called “circles” algorithm. The idea of this algorithm is to randomly choose many points in the initially flat terrain. Then, all vertices within a fixed size circle around these randomly chosen points are perturbed upward (or downward) to produce a round bump. Points closer to the centre of the circle are higher than those at the edge. After numerous such circles are created, eventually the terrain looks like that depicted above. Note that the number of iterations will need to be higher for larger surfaces, otherwise, the terrain will look sparse. Details of this algorithm can be found here: http://www.lighthouse3d.com/opengl/terrain/index.php?circlesRendering the terrainOnce the heightmap is loaded with values, the terrain needs to be actually rendered. You can use triangles or quads for this (at your discretion). You can also use triangle or quad strips – these primitives may make rendering the terrain easier. To render the terrain, you need simply index the heightmap for every xz vertex, and use the corresponding y value. To colour the terrain, you can initially use grayscale colours (as shown above) corresponding to the height of the vertex. Assuming there is a maximum and minimum height in your terrain, treat the lowest height as a value of 0 and the highest height as a value of 1. Then simply use the height value as the RGB colour value for each vertex. For lighting purposes, you can use a material colour of your choice. Other Necessary Functionality•Interactive viewpoint controlPressing the arrow keys should rotate the viewpoint. The left and right arrow keys should rotate the scene about the y axis, while the up and down arrow keys should rotate about the x axis (to some limit to prevent flipping the camera upside down). •Wireframe representationPressing the ‘w’ key should toggle wireframe mode between three options. The first (and default) setting is solid polygons (shown above). The second setting should display only the wireframe version of the terrain. The third setting should display both the solid polygons and the wireframe. You can use glPolygonMode to toggle the rendering settings for polygons. (Note that the third option will likely require you to render the entire scene twice!). •Lighting Implement lighting in the scene, which can be toggled with the L key. Note that this means you will need to compute surface normals for each face of the terrain (Hint: Write a function to do this once immediately following creation of the terrain). You should support two point light sources, initially positioned above opposite corners of the terrain. The colour of the lights is up to you. The position of the lights should be user controllable (i.e., by pressing keys). •Shading Provide the option to toggle between flat shading and Gouraud shading. •Reset – “R” key Pressing the “r” key should generate a new random terrain using the heightmap generation algorithm. •Graphics FeaturesYou should use backface culling and double buffering. The program should run in a window (i.e., not full screen). Multi Listed: Pressing “t” key draws the terrain using triangles (strips), pressing “y” key draws the same terrain using Quad (strips). To illustrate how the lighting is affected between triangles and quads. Extra FeaturesImplement two of the following extra features. Implement a third feature for bonus marks.1. Improved CameraImprove viewpoint control by adding a fully interactive camera. This should allow you to move the camera viewpoint to arbitrary points in the scene, and rotate it around its internal xyz axis. 2. Additional terrain algorithm(s)Add support for an additional terrain generation algorithm. Examples include the fault algorithm and the midpoint displacement algorithm. Note that you can select this option twice, i.e., for both of your extra features. See http://www.lighthouse3d.com/opengl/terrain/index.phpfor details of these algorithms. You can also create your own terrain algorithm. 3. Display 2D terrain overview Display a second GLUT window, and draw a 2D overhead representation of the terrain in this window. For example, if your terrain is 300x300 vertices, this 2D view would be 300x300 pixels in size. Each pixel in the view would be coloured according to the grayscale colours described above, i.e., using the height for the colour value. 4. Terrain modificationAllow users to interactively modify the terrain once it is created. Note that this will most likely be easier if you also implement Extra Feature #3 (2D terrain overview) above. By left clicking the mouse on the terrain (or in the 2D overview, if applicable) the terrain should bump upward, i.e., add a new circle according to the circles algorithm. Right clicking should perform the inverse operation, i.e., add a “dent” (push the terrain downward). 5. Add a characterAdd a character (or characters) to the scene. These may be controlled by the user, or may move around according to a random walk algorithm. The character(s) should appear to move around on the terrain, i.e., their height should be determined by the height of the terrain at the point they are moving across. One idea here would be to combine the snowman tutorial with your assignment, and have a number of randomly moving snowmen moving around on the terrain. Note that the character need not be animated, i.e., simply sliding across the terrain surface is fine! 6. Load heightmaps from image filesSince the heightmap is simply a 2D array of height values, it is possible to load grayscale images and use each pixel colour as a height value (again, according to the colour algorithm given earlier). For these purposes, you may use an image library, or image loading code. Be sure to cite your sources to avoid academic misconduct charges. We will also discuss the loading of a specific image file format (the PPM file) later, but this may not be soon enough. 7. Improved map colouringColour your terrain according to topographic maps. The lowest parts should be shades of green, and higher parts should become progressively more orange/red. The highest points (mountains) should be gray. See here for details: http://en.wikipedia.org/wiki/Hypsometric_tints. 8. Your own groovy featureImplement something along the lines of items 1 – 7 listed above of your own design. Be sure to document any references you use, and clearly indicate what this feature does.

SanjoyNathsTrigonoFractoGraphy Started with Analysis of operators and Fractal natures of Growth in Trigonometric Geometries Due to Sanjoy Naths Theory Of Geometrifying Trigonometry(C) . Some interesting facts behind the De Moivres Theorem with the light of Geometrifying Trigonometry(C) is that we have now special arrangements of different symmetric settings of multiplications and divisions which are both the * operations where division reverses the duplets of GT_Query_Strings(C) and continue with same kind of Align Scale To Fit systems where we see that ∞(ALT+236) type of fundamental multiplication operator will always expand the systems of Geometrifying Trigonometry NARRAYS(C) [N ARRAY ARRANGEMENTS OF ALIGNED SHAPES OF Geometrifying Trigonometry(C) LOCKED SETS(C)] where from the observations on Debashis Bhunias AUTOLISP outputs for the Sanjoy Nath's Geometrifying Trigonometry(C) Algorithms on Locked Sets(C) we can see that there are some expanding of shapes outlines nature present in ∞(ALT + 236) operations on Sin(Θ) and on Cos(Θ) .We call that as SinSpansion or CosSpansion , and the cases of ∞ operations on Sec(Θ) we call that SecSpansions . Similarly there are cases of TanSpansions , CosecSpansions , CotSpansions . Normally we have never seen any kind of contraction due to Union Outline Operation on GeometrifyingTrigonometry(C) Narays(C) but keeping intact in size of outlines with that of Seed Triangle [SEED_TRIANGLE(C) is the smallest possible basis LOCKED_SET(C) of GeometrifyingTrigonometry(C)] is the invariant nature of NARRAYS_OUTLINES(C) [We need to check for INTERSECTION_OF_NARRAYS(C) called NARRAYS_INLINES(C)] which are Contractions of Narrays(C) instead of Expansions of Narays due to merging. These are called as SinTraction , CosTraction,TanTraction,CosecTraction,SecTraction,CotTraction. We have several kinds of theorems on Geometrifying Trigonometry Operator Arithmatics where only expansions are possible and some of the operators sequences have very interesting properties of contraction of NARRAYS(C) merging which we will study in different theorems of Geometrifying Trigonometry.Very interesting natures of overlaps and the merging orientations exposes several insights hidden inside De Moivres Theorem which was vanished due to over usages of complex numbers.Complex number is a very useful tool in Current mathematics which was once called DOUBLE ALGEBRA due to DE MORGAN , has taken a large space of mathematics but that hides many of possible geometric interpretations and hides secrets inside its invisible ARGAND PLANE. Sanjoy Nath's Geometrifying Trigonometry(C) is exposing these hidden arrangements on 2D Euclidean Plane through the insertion of concept of LOCKED_SET(C) and through the very new operation called ALIGN_AND_SCALE_TO_FIT with four different possible symmetric arrangements which are very natural to common sense without any doubt.The big geometry giant Autodesk has even understood the importance of this operation long time back.This operation came to dilemma when Sanjoy Nath's Geometrifying Trigonometry(C) appeared with all possible forms of symmetric arrangements possible due to ALIGN_AND_SCALE_TO_FIT operation redefined with MINIMUM_ENERGY_ROTATION_WHILE_PIVOTING ∞ (ALT + 236) and consecuitive three other 3 operations (ó , ö , ô(not taken here) , ò) of mirroring about symmetric axis of merged line revamped the GEOMETRIZATION or GEOMETRIFICATIONS of many hidden REAL PICTURES on 2D REAL EUCLIDEAN PLANE which were hidden inside ARGAND PLANES for many years.Lets see the playground of these Theorems on SinCpansions , CosSpansions , TanSpansions , CosecSpansions , SecSpansions , CotSpansions , SinTractions , CosTractions , TanTractions , CosecTractions , SecTractions , CotTractions in System Theory , Chaos Theory , through the study of dynamics of arrangements of different line segments in Geometrifying Trigonometry(C) systems of Picture framework on Trigonometric Objects.

Geometrifying Number Systems replaces all Rational numbers as the best prime ratio of two numbers and so that numbers can get represented as Tan(Θ) forms which ultimately converts the world into Sanjoy Nath’s Geometrifying Trigonometry(C) forms which is very Common Sense provoking facts.Some interesting facts behind the De Moivres Theorem with the light of Geometrifying Trigonometry(C) is that we have now special arrangements of different symmetric settings of multiplications and divisions which are both the * operations where division reverses the duplets of GT_Query_Strings(C) and continue with same kind of Align Scale To Fit systems where we see that ∞(ALT+236) type of fundamental multiplication operator will always expand the systems of Geometrifying Trigonometry NARRAYS(C) [N ARRAY ARRANGEMENTS OF ALIGNED SHAPES OF Geometrifying Trigonometry(C) LOCKED SETS(C)] where from the observations on Debashis Bhunias AUTOLISP outputs for the Sanjoy Nath's Geometrifying Trigonometry(C) Algorithms on Locked Sets(C) we can see that there are some expanding of shapes outlines nature present in ∞(ALT + 236) operations on Sin(Θ) and on Cos(Θ) .We call that as SinSpansion or CosSpansion , and the cases of ∞ operations on Sec(Θ) we call that SecSpansions . Similarly there are cases of TanSpansions , CosecSpansions , CotSpansions . Normally we have never seen any kind of contraction due to Union Outline Operation on GeometrifyingTrigonometry(C) Narays(C) but keeping intact in size of outlines with that of Seed Triangle [SEED_TRIANGLE(C) is the smallest possible basis LOCKED_SET(C) of GeometrifyingTrigonometry(C)] is the invariant nature of NARRAYS_OUTLINES(C) [We need to check for INTERSECTION_OF_NARRAYS(C) called NARRAYS_INLINES(C)] which are Contractions of Narrays(C) instead of Expansions of Narays due to merging. These are called as SinTraction , CosTraction,TanTraction,CosecTraction,SecTraction,CotTraction. We have several kinds of theorems on Geometrifying Trigonometry Operator Arithmatics where only expansions are possible and some of the operators sequences have very interesting properties of contraction of NARRAYS(C) merging which we will study in different theorems of Geometrifying Trigonometry.Very interesting natures of overlaps and the merging orientations exposes several insights hidden inside De Moivres Theorem which was vanished due to over usages of complex numbers.Complex number is a very useful tool in Current mathematics which was once called DOUBLE ALGEBRA due to DE MORGAN , has taken a large space of mathematics but that hides many of possible geometric interpretations and hides secrets inside its invisible ARGAND PLANE. Sanjoy Nath's Geometrifying Trigonometry(C) is exposing these hidden arrangements on 2D Euclidean Plane through the insertion of concept of LOCKED_SET(C) and through the very new operation called ALIGN_AND_SCALE_TO_FIT with four different possible symmetric arrangements which are very natural to common sense without any doubt.The big geometry giant Autodesk has even understood the importance of this operation long time back.This operation came to dilemma when Sanjoy Nath's Geometrifying Trigonometry(C) appeared with all possible forms of symmetric arrangements possible due to ALIGN_AND_SCALE_TO_FIT operation redefined with MINIMUM_ENERGY_ROTATION_WHILE_PIVOTING ∞ (ALT + 236) and consecuitive three other 3 operations (ó , ö , ô(not taken here) , ò) of mirroring about symmetric axis of merged line revamped the GEOMETRIZATION or GEOMETRIFICATIONS of many hidden REAL PICTURES on 2D REAL EUCLIDEAN PLANE which were hidden inside ARGAND PLANES for many years.Lets see the playground of these Theorems on SinCpansions , CosSpansions , TanSpansions , CosecSpansions , SecSpansions , CotSpansions , SinTractions , CosTractions , TanTractions , CosecTractions , SecTractions , CotTractions in System Theory , Chaos Theory , through the study of dynamics of arrangements of different line segments in Geometrifying Trigonometry(C) systems of Picture framework on Trigonometric Objects.