Digital Media Dr. Jim Rowan ITEC 2110

So far… We have compared bitmapped graphics and vector graphics We have discussed bitmapped images, some file formats and some file compression techniques Today we are going to talk in a bit more detail about vector graphics Later we will cover Color Then 3D vector graphics

Vector Graphics… An elegant way to construct digital images that can have a compact representation are scalable have access to the objects And mandatory for 3-D modeling

First… Coordinate systems

Coordinate systems Bitmapped pixel coordinates (integer) x y 4,0 4,1 4,2 4,9 3,0 3,1 3,2 3,9 0,0 0,1 0,2 0,9 4 3 x 2 1 1 2 3 4 9 y

Coordinate systems bitmapped 4 3 x 2 1 1 2 3 4 9 y A= ( , ) B= ( , ) C= ( , ) D= ( , ) E= ( , )

Coordinate systems Vector graphics coordinates (real values) A point is defined by its x and y coordinate y (x,y) Can be fractional Can be negative 2 (1.41, 1.74) 1 1 2 3 x

Coordinate systems Vector graphics coordinates (real values) A displacement (distance between points or movement from one point to another) can be defined by a pair of points y displacement from point 1 to point 2... displacement = [(x2 - x1), (y2 - y1)] = (3.12 - 1.41, 0.95 - 1.74) (1.71,-0.79) point 1 2 (1.41, 1.74) 1 point 2 (3.12, 0.95) 1 2 3 x

AKA vector Vectors have magnitude (length) and direction This vector goes down 0.79 and to the right 1.71 It is a two dimensional (x&y) vector that goes down and to the right (1.71,-0.79) y 2 (1.41, 1.74) 1 (3.12, 0.95) 1 2 3 x

Why is it called vector graphics? Another grandfathered term From the time when displays were directly “steered” by their programs Give the display two points and it would move the beam from one point to the other drawing a line... This movement could be described as a vector since it has magnitude (length) and direction (from one point to the other)

Absolute vs Window coordinates rendering software renders images in a window windows can be moved around and... the rendering program only knows where the object is relative to the window it is in and… rendering software does not know where the window is on the screen so… a coordinate transformation must be performed

Absolute vs Window coordinates coordinates: measurement back to the upper left hand corner of the screen relative (to the window) coordinates measurement back to the upper left hand corner of the window to convert relative to absolute, add the relative coordinates to the absolute coordinate of the upper left hand corner of that window

Absolute & Relative Coordinates

The Bounding Box It’s a way to locate an object in space what point is used to place an object? the center of the object’s mass? the upper left corner? the lower right corner? images can be contained inside a “bounding box” which is the smallest box that contains all the points found in an object

Bounding Box x (0,0) desktop screen window bounding box y (100,103) (410,290) window 1 (210,175) (760,570)

Vector graphics Stores shapes (like a rectangle) very economically in the form of formulas or equations of geometric shapes Since a line segment can also be completely described by its endpoints… In computer graphics a line is defined by a line segment (i.e. it has endpoints)

Here’s the vector we saw earlier defined by it’s two endpoints 2 (1.41, 1.74) (3.12, 0.95) 1 1 2 3 x

To display a vector graphic you need to convert the vector graphic line to a bitmapped graphic… which presents problems!

Convert Vector to Bitmapped Visually Convert Vector to Bitmapped Visually... “completely cover the vector with pixels” 2 1 1 2 3 x

Vector to Bitmapped 2 1 1 2 3 x

The artifact created: A jagged line… This is “aliasing” 2 1 1 2 3 x

Aliasing(vector) When converting a vector graphic to a bitmapped graphic we can’t create a perfect representation What we end up with is a bitmapped version of the vector It’s not really the original but rather an alias of the original version Can have negative effects

Aliasing (bitmapped) When we view a bitmapped digital photograph on a display, the reconstruction is performed by a display device, and by our eyes and by our brain. If the reconstructed image differs from the original image, we are seeing an alias. http://en.wikipedia.org/wiki/Aliasing Can have negative effects

To combat negative effects of aliasing? anti-aliasing These are techniques to mitigate the affect of aliases “Smoothes” the edges of jagged lines How does this work?

Using anti-aliasing techniques on our original line our pixellated line to be displayed (the external model) is in black 2 1 1 2 3 x

combating aliases: anti-aliasing techniques the original vector graphic line stored in the internal model is in red our pixellated line to be displayed (the external model) is in black 2 1 1 2 3 x

combating aliases: anti-aliasing techniques 2 1 1 2 3 x

combating aliases: anti-aliasing techniques “average the grayness” 2 1 1 2 3 x

So far we have just looked at a line The line was stored as its endpoints What about other shapes?

Shapes made from connected lines connected lines are stored as a polyline internally the polyline is stored as a series of points closed polylines form a shape an open polyline is just a jagged line

rectangles and squares rectangles can be described by two corners squares are special cases of the rectangle

ellipses and circles ellipses can be described by two points circles are special cases of the ellipses they are stored as a single point http://en.wikipedia.org/wiki/Ellipse

vector graphics: drawing smooth curves Question: How would you draw a curve using a computer with a mouse? You can’t draw smooth lines very easily A line tool with handles (based on the Bezier curve) can be manipulated by those handles

Lines and curves Bezier curves can be smoothly joined together An anchor point is the point where one joins the other When a curve closes on itself it is considered a closed curve When it doesn’t it’s just an open curve

Lines and curves Closed (and open for that matter) lines can be filled solid color, pattern or gradient (linear or radial) Lines can have different ends mitre, rounded, square, bevel

The language of Manipulating objects… Translation: is a simple up/down side-to-side movement Scaling: make bigger or smaller Rotation: about a point Reflection: about a line

3-D? Way more complex than 2-D 3-D shapes (objects) are defined by their surfaces Made even more complicated by the fact that a 3-D object inside the computer must be translated into 2-D to be rendered on a computer screen... This results in the need to specify the viewpoint

Questions?