roundedRect can draw a rectangle of any shape and size and is about 25 lines of code long- it is versatile and animatable.
Frame 1 Seeing and Reality
We do not see the world as it really is.
A plan view of a railway track is shown on the left.
The distance between the rails is constant, the width, length and separation of the sleepers are also constant.
The view of the track on the right is what we see.
The rails converge and meet at a vanishing point on the horizon.
The width, length and separation of the sleepers diminish as they get further away from us,as does their thickness.
The colours of the track elements become less distinct as they get further away from us.
All the track elements vanish at the vanishing point on the horizon.
Our brain processes the light it receives through our eyes and gives us a perception of reality.
The operation of a camera is based on human vision- it produces an image of a scene as a human would see it.
When artists draw on canvas they draw what they see, that is, what they perceive.
The track on the right gives a sense of depth, it gives the canvas a 3D effect.
Figure 2 Diminuition and the Cone of Vision
Frame 2 The Picture Plane and Diminution
An artist creates a 3 dimensional picture on a canvas- the canvas is also called the picture plane.
In the diagram the red vertical line represents the edge of a picture plane.
The eye is looking at the picture plane, which is transparent, like a thin sheet of glass.
Four vertical posts, a,b,c and d are visible to the eye. The post are separated by a distance pSep and they have a height H.
Light travels from the posts to the eye and on its way it passes through the picture plane.
The eye is a distance D from the picture plane, each post is visible to the eye, they are not quite in line with each other.
An artist would draw each post on the picture plane with a different height, to create a 3D effect.
This diminution of the posts on the canvas is illustrated in the animation.
Frame 3 The Visual Angle and Diminution
We shall consider 4 rays of light that travel to the eye from posts a,b,c and d.
We have assumed that each of the rays enter the eye on the Central Ray of Vision, which is vitrually the case.
Each of the rays subtends an angle of vision α relative to the Central Ray of Vision.
The angle of vision for post a is αA, for post b it's αB, for post c it's αC and for post d it's αD.
Each ray of light passes through the picture at different heights relative the Central Ray of Vision.
These heights are ha, hb, gc and hd. Note that ha will be less than hd.
An artist would draw the heights of the posts on the picture plane as ha, hb, hc and hd.
The further away to posts are away from the picture plane the smaller they appear, the visual angle is smaller.
A post on the horizon woould have zero height, its visual angle woul be zero.
Frame 1 The Cone of Vision
The diagram shows the side view and top view of a face, with light rays travelling towards them.
The light rays are on the outside surface of a cone, which is called the cone of vision.
The small red circles represent the end view light rays travelling along the outside of the cone of vision.
The small red circle at the centre of the cone of vision is called The Central Visual Ray.
The rays close to the central visual ray are in focus, we can see with them clearly.
If look at the words "in focus" in the sentence above they are clearly in focus.
If you do not move your head or eyes, words even a short distance away are not so clear: words further away are more out of focus.
We can see using light rays that are inside the cone of vision in focus provided they are close to central visual ray.
Light rays that fall on our eyes towards the edge of the cone of vision generate our peripheral vision.
Figure 3 The Operation of the Human Eye
Frame 2 Image Formation by the Human Eye
The animation shows how 2 light rays travel from the post and produce an image on the retina.
One ray travels from the bottom of the post along the path of the central ray of vision.
The ray travels directly through the eye lens, it is not deflected within the eye.
It defines the bottom of the post image on the retina.
The other ray travels from the top of the post and enters the eye through the pupil.
It is focused on the retina and produces the top of the post image on the retina.
This ray is bent, that is refracted by the lens and substances in the eye.
Numerous rays of light travel from the post, enter the pupil, and form an image of the post on the retina.
The image is created mainly by the cones near the centre of the retina and form a coloured image.
The process is continuous, light is being reflected from the post, instant by instant, so the image is 'redrawn' millions of time a second.
Only the reflected light that enters the eye through the pupil is used to form the image.
Rays of light that fall on the face make it warm, but they do not contribute to vision.
Frame 1 The Main Elements of the Human Eye
The figure shows the side view of the right eye of a human being. The human eye is about 2cm in diameter.
The side view of a green post is also shown which is some distance from the eye.
The figure is not to scale, the eye has been enlarged so that its key elements can be seen and identified.
The height of the post has been reduced so that it fits on the canvas.
The Lens, the Pupil and the Iris allow light to enter the eye and be focused on the retina.
The light is focused on rods and cones on the retina which are sensistive to light.
There are more cones than rods in the central region of the retina, but outside the central region there are more rods than cones.
Electrical signals generated by the rods and cones pass along the optic nerve to the brain.
The signals are processed by the brain to produce the image of the post that we see.