JMU Lecture 3: Transforms 1

Principles of Interactive Graphics CMSCD2012

Dr David England, Room 711, ex 2271 d.england@livjm.ac.uk

http://java.cms.livjm.ac.uk/homepage/staff/cmsdengl/Teaching/cmscd2012/

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Today’s Lecture and Lab

Review of Tutorial: Circle drawing

This Week Transforms

Today’s tutorial: Transforms in L:\cd2012\transform.cpp

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Review of Tutorial

Last week we looked at a circle drawing algorithm which you translated from pseudo-code to C/C++

The algorithm calculates the points for one octant. The remaining points are generated by symmetry

L:\cd2012\circles.cpp has the working solution

The function circle(int x_centre, int y_centre, int radius) generates the octant points

plot_circle_points() generates the complete circle

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Transforms

So far everything we have drawn has been relative to the origin, 0,0,0.

This would make complex scenes hard to managed Most 3D graphics API’s have functions for

Translating (moving) in x, y and z Scaling, either

making objects smaller or larger of flipping them over

Rotation about an axis Transforms in OpenGL are part of the current graphics

context - why is this important?

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Transform functions: Translation

We can use the glTranslated(x,y,z) function to change the current drawing location

For exampleglTranslated(10.0, 10.0, 0); glRecti(0,0, 15, 10)

10

10(x1,y1)

(x2,y2)

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Transform functions: Scaling

Similarly we can change the relative size of the drawn objects with glScaled(x,y,z)

Where the sizes are multiplied in the relevant directions by x, y and z

glScaled(2.0, 2.0, 0); glRecti(0,0, 15, 10)

30

20

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Transform functions: Rotation

We can also rotate objects about the axes x,y and z with glRotated(angle, x, y, z)

For example glRotated( 45.0, 0.0, 0.0, 1.0); glRecti(0,0, 30,20)

20

30

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Transform functions: Combinations

Transforms can be combined but the final effect depends on the order of the transformations

10

20

A

B A: Translated then rotatedB: Rotated then translated

With B we have flipped the X,Y axes around by 45 degrees

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Transform functions: Combinations ...

Successive transforms are cumulative Each translation, rotation and scaling will work relative to

the last transformation function we used This is because there is a transform matrix which is part of

the current graphics context The transform matrix is a 4x4 array of values which is used to

re-calculate how the current drawing operation will be translated, rotated and/or scaled

We can reset the 4x4 matrix back to the origin values by calling glLoadIdentity()

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Transform functions: Combinations ...

We can use the accumulation of transform operations to draw a set of connected objects in the same location, e.g. A assembly of parts like a car wheel: tyre, brakes, hub

We can then switch off the accumulated transforms when we wish to move on to drawing another collection of objects

Planning the drawing of a complex object is then a matter of breaking it down into smaller collections where each smaller part shares a common set of

transforms A common problem is loosing track of which transforms are

being applied

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Transform functions: Combinations ...

The file L:\cd2012\transform.cpp has examples of Drawing a translated rectangle Drawing a translated and scaled rectangle relative to the

first Resetting the transform matrix Drawing a rectangle translated and rotated relative to the

origin The tutorial will explore what happens when changes are

made to transform.cpp

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