COIS712/ECOM7087CO1S800 Computer Graphics -Principles Systems Advanced Computer Graphics and Multimedia Advanced Computer Graphics and virtual simulation Chapter 4 Graphics Output Primitives (PartIl
COIS712/ECOM708/COIS800 Computer Graphics – Principles & Systems Advanced Computer Graphics and Multimedia Advanced Computer Graphics and Virtual Simulation Chapter 4 Graphics Output Primitives (Part II)
Outline Open gl Curve Functions fill-Area primitives ° Polygon FillAreas Open gl Polygon Fill-area Functions o Pixel Array Primitives ● Character primitiⅤes Open gL functions ° OpenGL Display lists
Outline OpenGL Curve Functions Fill-Area Primitives Polygon FillAreas OpenGL Polygon Fill-area Functions Pixel Array Primitives Character Primitives OpenGL functions OpenGL Display Lists 2
Chapter 4 Graphics Output Primitives(Part D) OpengL Curve Functions Fill-Area Primitives and Polygon FillAreas
Chapter 4 Graphics Output Primitives (Part II) OpenGL Curve Functions Fill-Area Primitives and Polygon FillAreas 3
OpenGL Curve Functions GLu(OpengL Utility) functions BD Quadrics(Spheres, Cylinders) Rational B-Splines(circles, ellipse, Bezier curve) (有理B樣條) gluSphere/ glu cylinder/ gluDisk NURBS(non-uniform rational B-splines) GLuT (Open gL Utility Toolkit)functions BD QuadricsSpheres, Cones etc. glutSolidSphere/glut Wire Sphere glutSolid Cone, glut SolidTorus Approximate a simple curve using a polyline o The more line sections, the smoother appearance of the curve. Write your own curve-generation algorithms Camputer Graphics with Open GL, Third Edition, by Donald Hearn and M. Pauline Baker ISBN0-13-0-15390-7o 2004 Pearson Education, Inc, Upper Saddle River, NJ. All rights reserve
OpenGL Curve Functions GLU (OpenGL Utility) functions: 3D Quadrics (Spheres,Cylinders) Rational B-Splines (circles, ellipse, Beziercurve) (有理B樣條) NURBS (non-uniform rational B-splines) GLUT (OpenGL UtilityToolkit) functions: 3D Quadrics (Spheres, Cones etc.) Approximate a simple curve using a polyline The more line sections, the smootherappearance of the curve. Write your own curve-generation algorithms (By Mark Kilgard) gluSphere/gluCylinder/gluDisk… 4 glutSolidSphere/glutWireSphere, glutSolidCone, glutSolidTorus,…
Fill-Area Primitives ●Fill( Filled)Area An area filled with some solid color or pattern To describe the surfaces of solid objects Most graphics library routines don t support arbitrary fill shapes A fill area is required to be specified as a polygon A set of polygon facets can approximate a curved surface(a polygon mesh), which can be called as SurfaceTessellation
Fill-Area Primitives Fill (Filled)Area An area filled with some solid color orpattern To describe the surfaces of solid objects Most graphics library routines don’t support arbitrary fill shapes. A fill area is required to be specified as a polygon. A set of polygon facets can approximate a curved surface (a polygon mesh),which can be called as SurfaceTessellation. 5
Polygon Fill Areas Polygon a plane figure specified by a set of three or more vertices. thatare connected in sequence by straight-line segments(edges) The interior angle is the angle inside the polygon boundary that Here refer only to those without is formed by two adjacent edges crossing edges: simple(standard) DORgon Polygon classifications 180° All interior angles are less than or equal to 180 degrees Concave Polygon(凹) A convex polygon(a)and a concave on Otherwise
Polygon Fill Areas A convex polygon (a) and a concave polygon (b) The interior angle is the angle inside the polygon boundary that is formed by two adjacent edges. Polygon A plane figure specified by a set of three or more vertices, thatare connected in sequence by straight-line segments (edges). Here refer only to those without crossing edges: simple (standard) polygon Polygon Classifications Convex Polygon (凸) All interior angles are less thanor equal to 180odegrees Concave Polygon (凹) Otherwise 6
Polygon Fill Areas Implementation consideration Some graphics packages including OpenGL, only support convex polygon for the fill algorithms. Generate a line segment For degenerate(退化) polygogerlapping edges. or edges with o. leng A set of vertices that are collinear(or that have repeated vertex positions To identify these cases, graphics systems usually leave these to the ● For concave polygons Implementation of fill algorithms and other graphics routines aremore complicated for concave polygons olit a concave polygon into a set of convex polygons
Polygon Fill Areas Implementation consideration Some graphics packages including OpenGL, only support convex polygon for the fillalgorithms. For degenerate (退化)polygons -- A set of vertices that are collinear (or that have repeated vertexpositions) --To identify these cases, graphics systems usually leave these to the programmer For concave polygons -- Implementation of fill algorithms and other graphics routines aremore complicated for concave polygons --To split a concave polygon into a set of convex polygons Generate a line segment Overlapping edges, or edges with 0 length 7
Identifying Concave Polygons Characteristics e At least one interior angle >1800 >180° Extension of some edges intersect other o Line segment of some pair of interior points intersects the be Doundary Mathematically The cross products of adjacent edges Convex: the same sign (E1XE2)>0 Concave: some are positive and (E2×E3)2>0 (E3×E4)20 (next slide for the detail) (E3×E)2>0 (E6×E1)2>0
Identifying ConcavePolygons Characteristics At least one interior angle>180o ; Extension of some edges intersect other; Line segment of some pair of interior points intersects the boundary. Mathematically The cross products of adjacent edges Convex: the same sign Concave: some are positive and some are negative (next slide for the detail ) 8
Splitting Concave Polygons a concave polygon with six edges Edge vectors for this polygon E1=(100)E2=( E E E3=(1,-10)E4=(030 E3=(3.00)E=(0-30) E2 E The cross product for two adjacent E dge vectors 0 E1XE2=(001)!E2×E3=(0,0,-2) Splitting a concave polygon using E E4=E4×E3=(009) the vector method (03)E5×E。E6×E1=(00.3) Determinant form i j k Spl(t, the polygon along the line of ax b= det al a2 a3 vector E2. The two new polygons b, b2 b3 9)ia2ba+jab1+ka1b2-iaab2-jay b,. are both convex
E2E3 = (0,0,−2) E4 E5 = (0,0,9) E6E1= (0,0,3) E1 E2 = (0,0,1) E3 E4 = (0,0,3) E5 E6 Split the =(0,0,9) polygon along the line of vector E2 .The two new polygons A concave polygon with six edges. Edge vectors for this polygon: E1 = (1,0,0) E2 = (1,1,0) E3 = (1,−1,0) E4 = (0,3,0) E5 = (− 3,0,0) E6 = (0,−3,0) The cross product for two adjacent edge vectors: Splitting ConcavePolygons Splitting a concave polygon using the vectormethod Determinant form are both convex. 9
Inside-Outside Tests ● Inside- Outside test rea-filling algorithms and other graphics processes often need to identify interior regions of objects For simple object, it is a straightforward process For complex objects, graphics packages normally use either 1.Odd-Even(a f-5)rule(Odd-Parity rule or Even-Oddrule) 2. Non-zero winding(環繞) number rule
Inside-Outside Tests Inside-Outside test ▪ Area-filling algorithms and other graphics processes often need to identify interior regions of objects. ▪ For simple object, it is a straightforward process. ▪ For complex objects, graphics packages normally use either: 1. Odd-Even (奇偶) rule (Odd-Parity rule or Even-Odd rule) 2. Non-zero winding (環繞) number rule 10
