SER431 Lecture 25

jgs SER 431 Advanced Graphics Lecture 25: Final Review Javier
Gonzalez-Sanchez javiergs@asu.edu PERALTA 230U Office Hours: By appointment

Javier Gonzalez-Sanchez | SER431 | Fall 2018 | 1 jgs
Calendar

jgs Midterm Topics

jgs Noise (Procedural Texture/Surfaces Generation)

Multi-scale Function Adding Noise over diverse frequencies and amplitudes )) * , * , * ( * ) , , ( 1 r scale t scale s scale noise amplitude r t s f i i i bands i i å = - =

Sum of Absolute Values Adding Noise over absolute values is Good for fire )) , , ( ( ) , , ( 1 r scale t scale s scale noise amplitude r t s f i i i bands i i å = - =

Marble Principle ))) , , ( ( * sin( ) , , ( 4 1 r scale t scale s scale noise amplitude s r t s f i i i i i å = - = Using sin( ) function plus noise

Marble Example § MarbleMap is from black to white § Scale scales [min, max] to [0,1] § u and v are in range [0,1] § Does not look that great, maybe a more complex color ramp is needed )) ) 5 . 11 , * 2 * 5 , * 2 * 5 ( * 2 * 6 * 20 sin ( ( ) , ( 4 1 ÷ ø ö ç è æ + = å = - v u PNoise u Scale MarbleMap v u Texture i i i i

Graphics https://www.youtube.com/watch?v=aviL3HX3UEc

jgs Collision (Axis-aligned bounding box)

§Axis-aligned Bounding Box (AABB) § An AABB is defined by its minimal and maximal positions in space Pmin=(xmin, ymin, zmin), Pmax = (xmax, ymax, zmax) § Calculate Initialize pmin to +infinite or the first vertex Initialize pmax to –infinite or the first vertex foreach vertex p do { if (p.x < pmin.x) then pmin.x = p.x if (p.y < pmin.y) then pmin.y = p.y if (p.z > pmax.z) then pmax.z = p.z }

AABB Calculate AABB Draw AABB with lines

jgs Shadows, Reflection, and Fog

Concepts § What is the shadow matrix? § What is the stencil buffer? § What is double blending and how to avoid it?

Step 2. init() void init() { // ... glClearStencil(0); }

Step 3. display() void display(void) { glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT | GL_STENCIL_BUFFER_BIT); glEnable(GL_STENCIL_TEST); glColorMask(GL_FALSE, GL_FALSE, GL_FALSE, GL_FALSE); // glColorMask controls with Stencil or Color buffer? glStencilFunc(GL_ALWAYS, 1, 1); glStencilOp(GL_REPLACE, GL_REPLACE, GL_REPLACE); // <Render stencil box>

glDisable(GL_DEPTH_TEST); glMatrixMode(GL_PROJECTION); glLoadIdentity(); glOrtho(-50.0, 50, -50.0, 50.0, 1.0, -1.0); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glPushMatrix(); glTranslatef(0, 0, 0); glBegin(GL_TRIANGLES); glVertex2f(-20.0, -20.0); glVertex2f( 20.0, -20.0); glVertex2f( 0.0, 20.0); glEnd(); glPopMatrix(); glEnable(GL_DEPTH_TEST);

// re-enable color and disable stencil glColorMask(GL_TRUE, GL_TRUE, GL_TRUE, GL_TRUE); glStencilFunc(GL_EQUAL, 1, 1); glStencilOp(GL_KEEP, GL_KEEP, GL_KEEP); // draw your colors here glDisable(GL_STENCIL_TEST); glutSwapBuffers(); }

Fog glEnable(GL_FOG); // specifies the equation to be used to compute the fog blend factor. // GL_LINEAR, GL_EXP, and GL_EXP2. // initial fog mode is GL_EXP glFogi(GL_FOG_MODE, GL_LINEAR); // the fog color. Color components are in the range [0,1]. // the initial fog color is (0, 0, 0, 0). GLfloat fogColor[4] = { 0.5, 0.5, 0.5, 1.0 }; glFogfv(GL_FOG_COLOR, fogColor); //Used in exponential fog equations. The initial fog density is 1. // Only nonnegative densities are accepted. glFogf(GL_FOG_DENSITY, 0.25); // the near distance used in the linear fog equation. The initial near distance is 0 glFogf(GL_FOG_START, 10.0); // the far distance used in the linear fog equation. The initial far distance is 1. glFogf(GL_FOG_END, 6000.0);

jgs Particle Systems

Particles § Emitter § Behavioral parameter of a particle (lifetime, initial velocity, spawning rate, color) § Equations

Graphics https://www.youtube.com/watch?v=aviL3HX3UEc

jgs Curves

All about Curves

Curves § What is a Curve? § What is Curvature? § Parametric Representation § Curve equation (general) § Control Graph § Control Point § Tangent

Curves § Explain C0, C1, C2 continuity § Explain similarities and differences of: Bezier, Hermite, Chaikin and B-spline Curves § What is a Blending Function? § Explain A-frame

Blending Functions Bezier § B0 (t)=(1-t)3 § B1 (t)=3t(1-t)2 § B2 (t)=3t2(1-t) § B3 (t)=(t)3 Cubic B-Spline § B0 (t)=((1-t)3)/ 6 B1 (t)=(3t3 -6t2 + 4)/ 6 B2 (t)=(-3t3 + 3t2 + 3t + 1) / 6 B3 (t)=(t)3 / 6

Blending Functions Hermite § B0 (t)= 2*t3 – 3*t2 + 1, § B1 (t)= -2*t3 + 3*t2, § B2 (t)= t3 - 2*t2 + t, § B3 (t)= t3 – t2

Apply Bezier Algorithm

Apply B-spline Algorithm

Apply Chaikin Algorithm Qi=3/4Pi + 1/4Pi+1 Ri=1/4Pi + 3/4Pi+1

jgs New Topics

jgs NURBS (Procedural Texture/Surfaces Generation)

Code // control points GLfloat ctlpoints[4][4][3] = { { { 20, 0, 10 },{ 0, 0, 10 },{ -5, 0, 10 },{ -10, 0, 10 } }, { { 20, 0, 5 },{ 0, 15, 5 },{ -5, 15, 5 },{ -10, 0, 5 } }, { { 20, 0, -5 },{ 0, 10, -5 },{ -5, 10, -5 },{ -10, 0, -5 } }, { { 20, 0, -10 },{ 0, 0, -10 },{ -5, 0, -10 },{ -10, 0, -10 } } }; GLfloat knots[8] = { 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 3.0 }; GLUnurbsObj *theNurb;

Code // init void init(void) { // Materials and Light GLfloat mat_diffuse[] = { 1.0f, 0.5f, 0.31f, 1. }; GLfloat mat_specular[] = { 0.5f, 0.5f, 0.5f, 1. }; GLfloat mat_ambient[] = { 1.0f, 0.5f, 0.31f, 1. }; GLfloat mat_shininess[] = { 100.0 }; glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT, mat_ambient); glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, mat_diffuse); glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, mat_specular); glMaterialfv(GL_FRONT_AND_BACK, GL_SHININESS, mat_shininess); glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glEnable(GL_DEPTH_TEST); glEnable(GL_AUTO_NORMAL); glEnable(GL_NORMALIZE); theNurb = gluNewNurbsRenderer(); gluNurbsProperty(theNurb, GLU_SAMPLING_TOLERANCE, 25.0); gluNurbsProperty(theNurb, GLU_DISPLAY_MODE, GLU_FILL); // }

// display void display(void) { // camera and others configurations here... // NURBS glColor3f(0, 1, 0); gluBeginSurface(theNurb); gluNurbsSurface( ... ); gluEndSurface(theNurb); // more ... }

Numbers to be considered // V_size curves with U_size control points each // V_size + ORDER knots per curve and // U_size + ORDER knots per inter-curve connection // offsets are V_size*3 and 3 // cubic equations ORDER = 4 GLfloat ctlpoints[U_size][V_size][3] = { … }; GLfloat vknots [V_size + ORDER] = { …}; GLfloat uknots [U_size + ORDER] = { …} gluNurbsSurface(theNurb,U_size + ORDER, uknots, V_size + ORDER, vknots, V_size * 3, 3, &ctlpoints[0][0][0], ORDER, ORDER, GL_MAP2_VERTEX_3);

Screenshot 6 curves 6 control points each 5 curves 6 control points each 4 curves 6 control points each

Problem A https://github.com/javiergs/SER431/blob/master/Lecture20/nurbs_surface_controlled.cpp

Problem A // NURBS // How many curves? How many control points per curve? // How many knots per curve? How many knots per inter-curve connection? // Order for U and V? // Offset for U and V? GLfloat ctlpoints[4][4][3] = { { { 20, 0, 20 } ,{ 0, 0, 20 },{ 0, 0, 20 } ,{ -20, 0, 20 } }, { { 20, 0, 0 } ,{ 0, 20, 0 },{ 0, 20, 0 } ,{ -20, 0, 0 } }, { { 20, 0, 0 } ,{ 0, 20, 0 },{ 0, 20, 0 } ,{ -20, 0, 0 } }, { { 20, 0, -20 } ,{ 0, 0, -20 },{ 0, 0, -20 } ,{ -20, 0, -20 } } }; GLfloat uknots[8] = { 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 3.0 }; GLfloat vknots[8] = { 0.0, 0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 3.0 };

Problem B https://github.com/javiergs/SER431/blob/master/Lecture20/nurbs_surface_controlled.cpp * There are 7 squares (i.e., 7 curves)in blue. * You need 8 control points per square; BUT since you want to close the curve. You may should need to add the first one again. Thus 8 + 1

Problem B // NURBS // How many curves? How many control points per curve? // How many knots per curve? How many knots per inter-curve connection? // Order for U and V? // Offset for U and V? const int V_size = 9; const int U_size = 7; const int ORDER = 4; GLfloat ctlpoints[U_size][V_size][3] = { { { 0, -4, 0 }, { -4, -4, 0 } ,{ -4, 0, 0 }, { -4, 4, 0 }, { 0, 4, 0 }, { 4, 4, 0 }, { 4, 0, 0 }, { 4, -4, 0 }, { 0, -4, 0 } }, { { 0, -2, 4 }, { -2, -2, 4 } ,{ -2, 0, 4 }, { -2, 2, 4 }, { 0, 2, 4 }, { 2, 2, 4 }, { 2, 0, 4 }, { 2, -2, 4 }, { 0, -2, 4 } }, { { 0, -4, 8 }, { -4, -4, 8 } ,{ -4, 0, 8 }, { -4, 4, 8 }, { 0, 4, 8 }, { 4, 4, 8 }, { 4, 0, 8 }, { 4, -4, 8 }, { 0, -4, 8 } }, { { 0, 0, 10 }, { 0, 0, 10 } ,{ 0 , 0, 10 }, { 0, 0, 10 }, { 0, 0, 10 }, { 0, 0, 10 }, { 0, 0, 10 }, { 0, 0, 10 }, { 0, 0, 10 } }, { { 0, -1, 12 }, { -1, -1, 12 } ,{ -1, 0, 12 }, { -1, 1, 12 }, { 0, 1, 12 }, { 1, 1, 12 }, { 1, 0, 12 }, { 1, -1, 12 }, { 0, -1, 12 } }, { { 0, -2, 14 }, { -2, -2, 14 } ,{ -2, 0, 14 }, { -2, 2, 14 }, { 0, 2, 14 }, { 2, 2, 14 }, { 2, 0, 14 }, { 2, -2, 14 }, { 0, -2, 14 } }, { { 0, -4, 16 }, { -4, -4, 16 } ,{ -4, 0, 16 }, { -4, 4, 16 }, { 0, 4, 16 }, { 4, 4, 16 }, { 4, 0, 16 }, { 4, -4, 16 }, { 0, -4, 16 } } }; GLfloat vknots[V_size + ORDER]= {0.0, 0.0, 0.0, 0.0, 2.0, 4.0, 4.0, 4.0, 6.0, 8.0, 8.0, 8.0, 8.0 }; GLfloat uknots[U_size + ORDER]= { 0.0, 0.0, 0.0, 0.0, 1.0, 3.0, 5.0, 6.0, 6.0, 6.0, 6.0 };

Review This https://github.com/javiergs/SER431/blob/master/Lecture08/reflection.cpp

jgs Fractals

jgs Case 1: Symmetrical Stack boxes

Code // create a pile of boxes as fractal void stackBoxes(float x, float y, float z) { if (y >= 0) { glPushMatrix(); glTranslatef(x, y*100, z*100/2); glCallList(display2); glPopMatrix(); stackBoxes(x-50, y-1, z-1); stackBoxes(x-50, y-1, z+1); stackBoxes(x+50, y-1, z-1); stackBoxes(x+50, y-1, z+1); } }

Case 1 Level = 0 Level = 1 Level = 2 Level = 3 Level = 4

Code vector <Line> thunderbolt; void createBolt(Vec3f p1, Vec3f p2, int level) { thunderbolt.push_back(Line(p1.x,p1.y,p1.z, p2.x,p2.y, p2.z)); for (int t = 0; t < level; t++) { int tam = thunderbolt.size(); Vec3f middle; int i; for (i = 0; i < tam; i++) { p1.x = thunderbolt[0].x1; p1.y = thunderbolt[0].y1; p1.z = thunderbolt[0].z1; p2.x = thunderbolt[0].x2; p2.y = thunderbolt[0].y2; p2.z = thunderbolt[0].z2; thunderbolt.erase(thunderbolt.begin()); middle = calculateMiddle(p1, p2, t); thunderbolt.push_back(Line(p1.x, p1.y, p1.z, middle.x,middle.y, middle.z)); thunderbolt.push_back(Line(middle.x, middle.y, middle.z, p2.x,p2.y, p2.z)); } // extension line Vec3f direction = middle - p1; Vec3f pin = middle + direction * 0.7; thunderbolt.push_back(Line(middle.x, middle.y, middle.z, pin.x, pin.y, pin.z)); } }

Case 1 Level = 0 Level = 1 Level = 2 Level = 3 Level = 10

Tree // full tree glNewList(FULLTREE, GL_COMPILE); glPushMatrix(); glTranslatef(0, -1, 0); fractalTree(0); glPopMatrix(); glEndList(); }

void fractalTree(int level) { long savedseed; if (level == MAX_LEVEL) { glPushMatrix(); glRotatef(random_number() * 180, 0, 1, 0); glCallList(STEMANDLEAVES); glPopMatrix(); } else { glCallList(STEM); glPushMatrix(); glRotatef(random_number() * 180, 0, 1, 0); glTranslatef(0, 1, 0); glScalef(0.7, 0.7, 0.7); glPushMatrix(); glRotatef(110 + random_number() * 40, 0, 1, 0); glRotatef(30 + random_number() * 20, 0, 0, 1); fractalTree(level + 1); glPopMatrix();glPushMatrix(); glRotatef(-130 + random_number() * 40, 0, 1, 0); glRotatef(30 + random_number() * 20, 0, 0, 1); fractalTree(level + 1); glPopMatrix();glPushMatrix(); glRotatef(-20 + random_number() * 40, 0, 1, 0); glRotatef(30 + random_number() * 20, 0, 0, 1); fractalTree(level + 1); glPopMatrix(); glPopMatrix(); } }

Disclaimer This list of topics is not Comprehensive For a full list of topics review lectures 1 to 24

jgs SER431 Advanced Graphics Javier Gonzalez-Sanchez javiergs@asu.edu Fall 2018 Disclaimer.
These slides can only be used as study material for the class SER431 at ASU. They cannot be distributed or used for another purpose.

SER431 Lecture 25

SER431 Lecture 25

Javier Gonzalez PRO

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Javier Gonzalez
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