One Point Perspective:
Two Point Perspective:
Isometric Drawing:
Orthographic Drawings
Geometric Net:
Cross Sections:
My Anamorphic 3-D Drawing Project:
Anamorphic: When an image is distorted because of projection, it is then rotated the angle of the image is changed to make the image look normal or ‘3D’. For example in the picture of the girl in the pool drawn by Julian Beever, if you are standing at the front of the picture looking at it, it looks like a girl in a pool. If you were to look at the picture upside down or from any other angle, it would look completely different and would be out of proportions.
("Anamorphic." Dictionary.com. Dictionary.com, n.d. Web. 21 Apr. 2014.)
("Anamorphic." Dictionary.com. Dictionary.com, n.d. Web. 21 Apr. 2014.)
During this project, we set up a picture frame, in a stand made from a cardboard box, and drew an image on the glass to project onto a piece of poster board. We then looked through the picture on the glass to draw points on the poster board. After drawing the points, we used a rule or meter stick to connect the points to make the picture we were projecting.
Our final product of the anamorphic drawing on the poster board is the result of the image on the glass being projected onto the paper. To create the drawing, one person was sitting in a chair looking at the picture on the glass that was being projected onto the poster board on the table behind it. The partner in the chair would tell the other partner were to draw a point on the poster board based on where it was being projected. Our final image is result of projection because the small image on the picture frame glass, is elongated and stretched creating a picture that fits the poster board.
During this project, my partner and I had a difficult keeping the points we had drawn on the poster board lined up with the image on the glass. Because of this, we had to do a lot of erasing to finally get all of them lined up to make the image.
Our final product of the anamorphic drawing on the poster board is the result of the image on the glass being projected onto the paper. To create the drawing, one person was sitting in a chair looking at the picture on the glass that was being projected onto the poster board on the table behind it. The partner in the chair would tell the other partner were to draw a point on the poster board based on where it was being projected. Our final image is result of projection because the small image on the picture frame glass, is elongated and stretched creating a picture that fits the poster board.
During this project, my partner and I had a difficult keeping the points we had drawn on the poster board lined up with the image on the glass. Because of this, we had to do a lot of erasing to finally get all of them lined up to make the image.
Data Collection:
East:1. Tan21= H/X
Tan20= H/X+55 2. XTan21=(X+55)Tan20 (XTan21=H) 3. XTan21=XTan20+55Tan20 4. XTan21-XTan20=55Tan20 5. X(Tan21-Tan20)=55Tan20 6. X=55Tan20/(Tan21-Tan20) 7. X=53.156ft 8. Plug X into XTan21 (53.156Tan21) 9. H=25.904 |
West:1. Tan17=H/X
Tan15=H/X+90 2. XTan17=(x+90)Tan15 (XTan17=H) 3. XTan17=XTan15+90Tan15 4. XTan17-XTan15=90Tan15 5. X(Tan17-Tan15)=90Tan15 6. X=90Tan15/(Tan17-Tan15) 7. X= 638.286 8. Plug X into XTan17 (638.286Tan17) 9. H=644.092 |
South:1. Tan15= H/X
Tan6= H/X+143 2. XTan15=(x+143)Tan6 (XTan15=H) 3. XTan15=XTan6+143Tan6 4. XTan15-XTan6=143Tan6 5. X(Tan15-Tan6)=143Tan6 6. X=143Tan6/(Tan15-Tan6 7. X=92.295 8. Plug X into XTan15 (92.295Tan15) 9. H=98.063 |
Hexaflexagon:
My design for my Hexaflexagon uses a lot of line reflection to create that patterns. The line reflection is used so that when the Hexaflexagon would be constructed all the line would match up to make a shape. For the circular designs shown in the picture, I used a compass to measure and accurately draw the arcs on the diamond shaped sides of the Hexaflexagon. For the line designs in the other picture, I used a ruler and measured each colored segment so that I could replicate the pattern in each triangle.
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The part of the design that I like the most in my Hexaflexagon are the sections that make up the circles. I like these parts because they are bright colored they draw your eyes to it because of the shape. Refinements that I would make to the lines of symmetry would be to connect the lines of the circle over to the other section. If I were to refine the lines to make them meet up better. Something that I learned about myself through this activity is that when I draw circles on a Hexaflexagon, it can be mesmerizing when playing with it.
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Snail-Trail Graffiti GGB Lab:
To create this design, I would drag one of the six points around the screen. The remaining five points were synced with the one point and would do what that point was doing. Half of the points were reflected over the line next to it. The orange design reflected over the line making the purple pattern, green to light blue, blue to yellow.
I had fun during this lab in Geogebra because it was fun getting to play with the points and getting to move them around the page making cool designs. Through this lab, I learned that I really enjoy making patterns that reflect over lines and end up making a circular design. |
Two Rivers GGB Lab:
There is a sewage treatment plant at the point where two rivers meet. You want to build a house near the two rivers (upstream from the sewage plant, naturally), but you want the house to be at least 5 miles from the sewage plant. You visit each of the rivers to go fishing about the same number of times but being lazy, you want to minimize the amount of walking you do. You want the sum of the distances from your house to the two rivers to be minimal, that is, the smallest distance.
The Burning Tent GGB Lab:
A camper out for a hike is returning to her campsite.The shortest distance between her and her campsite is along a straight line, but as she approaches her campsite, she sees that her tent is on fire! She must run to the river to fill her canteen, and then run to her tent to put out the fire. What is the shortest path she can take? In this exploration you will investigate the minimal two-part path that goes from a point to a line and then to another point.
In this picture, the scenario is shown where the person would not have the smallest amount to run to the river then the tent. The reason that this scenario shown in the picture would not work is because the length from the river to the tent is much longer than from where the camper is standing to the river. The angle at which the person would be running to the river is much larger than the angle that the person would be running at when leaving the river to the tent.
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In this picture, the scenario is shown the person would have the smallest amount to run to the river then the tent. The reason that this scenario would work is because the length from where the camper is standing to the river and then the length from the river to the tent is the same length (or almost the same). This means that the angle that the person is running to the river and then leaving the river is the same. This makes the minimal distance that the person would have to run.
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