Undefined terms in Geometry

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Undefined terms in Geometry
Please write the sponge in the space
provided Sponge for Today What is perspective?
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Background Info

• The Renaissance was the beginning of a formal use
  of composition and perspective.
• The Renaissance (1400 - 1600) was a great rebirth
  of European learning and discovery.
• It ended 1000 years of superstition and ignorance
  that followed the fall of Rome.
• The Renaissance began in Italy and spread
  throughout northern Europe.
• Renaissance artist include Michelangelo and
  Leonardo da Vinci, scientists like Galileo, and
  writers like Shakespeare.

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Characteristics

• Renaissance artists
• investigating and representing the real world
• continued to depict religious subjects but also
  began to portray the human experience
• brought back the Greek classical ideals of ideal
  proportions (for depicting the human body as well
  as for architecture and painting)

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Linear Perspective

• Is based on the way human eye sees world-objects
  which are closer appear larger, and more distant
  objects appear smaller.
• Uses a vanishing point on the horizon line to
  create the illusion of space.
• Is created by drawing objects using orthogonal
  lines which lead to the vanishing point(s).

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Linear Perspective

• Perspective is a technique for representing
  3-dimensional space on a flat surface.
• During the Renaissance artists invented a
  mathematical system to show depth logically and
  consistently.
• System helped to create realistic art.

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1 point vs. 2 point

• In one-point perspective, the forms are seen face
  on and are drawn to a single vanishing point.
• Objects seen at an angle would be drawn with
  two-point perspective using two vanishing points.
  Often these vanishing points are "off the page".

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Other ways to Create Depth

• The ways that artists make things look deep
• Size objects appear smaller as they get farther
  away.
• Position objects appear higher on the page as
  they get farther away.
• Overlap Overlapping objects show which is
  farther.
• Detail Objects have less detail as they get
  farther away.
• Saturation of color Close objects are brightest
  and sharpest. Objects in the distance appear pale
  and washed out.
• Atmospheric perspective Objects in the distance
  may appear bluish.
• Warm colors advance/cool colors recede Warm
  colors may appear closer. Cool colors may appear
  farther away.

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Before the renaissance

• How did artist create depth?

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Is there Depth?
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How to find Vanishing pt

• Identify the horizon on artwork.

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How to find Vanishing pt

• Lines from objects to the horizon line create the
  vanishing point is clearly established.
• The lines leading to the vanishing point are
  called are called orthogonals.

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1 pt perspective Look

• A cube in one-point perspective the front face of
  the form is seen as the closest point.
• The number of sides visible, whether or not you
  see the top or bottom of the box depends on the
  angle from which you view it.

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Drawing a 1 pt Perspective object

• Step 1
• Orient your paper or draw a large rectangle on
  your board to represent a paper turned
  horizontally, or "landscape orientation."

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Lines, lines, lines

• Every line you make in one-point perspective will
  be vertical, horizontal or an orthogonal line
  (irregular shapes and lines can be dealt with
  later).
• Make the end of the ruler flush with the edge of
  the paper. This is one of the most important and
  most challenging skills! If lines are not exactly
  horizontal and vertical, your students' drawings
  will be skewed!

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Drawing a 1 pt Perspective object

• Step 2
• Draw a horizon line towards the top of the page
  and label it.

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Drawing a 1 pt Perspective object

• Step 3
• Draw the vanishing point in the center of the
  horizon line and label it.

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Drawing a 1 pt Perspective object

• Step 4
• Now draw a square or rectangle and label it
  "front face". Draw it in one of the lower corners
  so you have plenty of room to add more forms. You
  can continue to relate the drawing to the
  physical box model as you work.

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Drawing a 1 pt Perspective object

• Step 5
• Now connect three corners of your rectangle or
  square to the vanishing point. These are
  orthogonals. Draw lightly so you can erase!

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Drawing a 1 pt Perspective object

• Step 6
• Draw a horizontal line between the top two
  orthogonals where you want your form to end to
  make the top of the box.

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Drawing a 1 pt Perspective object

• Step 7
• Draw a vertical line down from the horizontal
  line to complete the side.

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Drawing a 1 pt Perspective object

• Step 8
• Erase the remaining orthogonals.

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Drawing a 1 pt Perspective object

• Step 10

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Drawing a 1 pt Perspective object

• Step 11

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Drawing a 1 pt Perspective object

• Step 12

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Drawing a 2 pt Perspective object

• Two-point perspective is useful to show an angle
  rather than face-on.
• Most lines are vertical or orthogonals drawn to
  two different vanishing points.

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Class Work

• Draw a 2 point perspective drawing using the
  directions provided

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Undefined terms in Geometry
Please write the sponge in the space
provided Sponge for Today What is perspective?
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Points, lines, Planes

• Locate use symbolic language
• A point
• A line
• Collinear points
• Noncollinear points
• A line segment
• A ray
• Opposite rays
• A plane
• Intersection of 2 lines
• Intersection of 2 planes

• Undefined terms in Geometry
• Label your shape and draw arrows as follows

l
P
? R
E
F
Draw arrows at the ends of your horizon
A
D
G
? X
B
C
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Points, lines, Planes

• Find point Q
• You describe a point by writing the word point
  and using a capital letter Point Q
• Find line l
• There are two different ways to describe a line
  1) naming any two points on the line with an line
  on top, or 2) writing line l
• Collinear points are points on the same linesuch
  as point P, point Q, and point R (need three pts)
• Noncollinear points are points NOT on the same
  linesuch as point D, point G, and point C (need
  three pts)

P
l
? Q
? Q
? R
E
F
A
D
G
? X
B
C
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Points, lines, Planes

• A line segment has two endpoints.
• You describe a line segment using two points with
  a segment on top
• A ray has one endpoint.
• You describe a ray by naming the initial point
  first and the directional point second with a ray
  on top
• Opposite rays look like a line
• A plane extends in four directions forever its
  a surface
• You describe a plane by naming three noncollinear
  points or by one capital letter
• Intersection of 2 lines
• Intersection of 2 planes

P
l
? Q
? R
E
F
A
D
G
? X
B
C