...models for bones of the human body utilizing medical imaging data. The human hand was chosen as the subject of the research. Computed Tomography (CT) imaging was chosen to provide a volumetric data set. This data set was visualized through an isosurfacing technique utilizing the marching cubes algorithm. The original CT data set contained slices that were not aligned with the natural orientation or long axis of the bones. Transformation matrices and linear interpolations were used to generate a data set of slices oriented along the natural axis of the bones. Contours were created on these slices through an edge-tracking method. B-Spline curves were then constructed utilizing the contour’s vertices as knot points. A consistent starting location was found on each closed B-Spline curve relative to its centroid. Points on the closed B-Spline curves were then...
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...y. So x is something that comes before y in time. Plot (a) seems do not have a correlation at all; there is no pattern to indicate where the data point lie. The points do not go in any particular direction; therefore this data has a correlation value of 0. No correlation occurs when there is no linear dependency between the variables. Plot (b) appears to have a positive correlation, although the data points are not very close together. Graph (b) would probably have a value of 0.3. A correlation is weaker the farther apart the points are located to one another on the line. Plot (c) You can see from the plot that these data don’t fit a straight line. There is a distinct bend near the left, and curve down to the right. When you have anything with a curve or bend, linear regression is wrong. This plot has a nonlinear relationship. Plot (d) While the points tend to be falling, it is a clearly negative relationship since points are not clustered as to show a clear straight line. It is a low negative correlation. Negative correlation occurs when an increase in one...
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...Geometry Notes First Class Point has zero dimensions Postulates/Axioms: statement we accept as being true without a proof Theorems/Corollaries: statement that must be proven before we accept it as being true Corollaries are spin off of another theorem Postulates * P1-1 Given any two points, there is a unique distance between them * P1-2 any segment has exactly one midpoint Theorem * T1-1 “Midpoint Theorem” If m is the midpoint of segment AB, then: 2AM=AB, AM=1/2AB and 2MB=AB, MB=1/2 AB Vocab: Collinear: points that are on the same straight line Noncollinear Points: Points that are not on same straight line Obliquely intercept: not at 90 degree angle Three positions for two lines in space 1. Skew lines: never intercept and not parallel. 2. Parallel Lines: never intercept 3. Intercepting lines: cross each other Planes Planes go on forever, never end, like lines. Line can be: * in plane * Intercept plan * Parallel with plane Two relationships for Planes 1) Parallel 2) Intercept Space contains all points Line with 4 colinear points Can name it line L, or take two points on the line and same it that way. AB, AC, AD, BC, BD, with arrows on top. Subsets of line. * Rays, has only one arrow on top cause starts at point, * Rays going in diff direction on line called opposite rays, same starting points, but opposite directions * Can’t change lettering around with rays cause first letter is...
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...nothing, an outline with no picture.” An inspiring quote from Milan Kundera. A man who sees the good in the bad and grabs ahold of all this good to see his straight line in life. Life’s line has edges, corners, walls, the right-way doors, and the bad-way doors, it has mountains, and hills, and u-turns, and rivers, and valleys, and every once in a while life has a straight line. Your straight line can be as long as one day, one week, one month, and even one second long and you determine that. You make your line and leave it here for everyone else to see. Make your line an obsession not a degression, a leader not a follower, straight not an empty mess. It’s your life and your line. Make it who you are not who you want to be. When you get to that curve or edge don’t give up. Giving up means you're a quieter and you’re not! When they tell you you can’t, tell them you can and show them you can, because everything is possible. Life is just one messed up line trying to tear you down. Don’t let it, make your line the way you want. Keep reaching for straightness and be the succeeder, and always remember straight lines do exist. You just have to make them exist. Make this your life and your...
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...equation to describe those parts would be r=1/N(1/d) In the case of the Sierpenski Triangle, a self repeating object, the equation is D = log (N) / log (1/r) (STSCI) The Koch Snowflake is designed by: * divide a line segment into three equal parts * remove the middle segment (= 1/3 of the original line segment) * replace the middle segment with two segments of the same length (= 1/3 the original line segment) such that they all connect (i.e. 3 connecting segments of length 1/3 become 4 connecting segments of length 1/3.) The top row of shapes is the pattern to make the snowflake with a triangle, the bottom shape is a blowup of the edge of the last figure shown. Its fractal dimension is given from the definition of the curve: N = 4 and r = 1/3 (remember 4 segments each 1/3 size of the original line segment). Dimension = log (4) / log (3) = 1.26 Another interesting property of the Koch Snowflake is that it encloses a finite area with an infinite perimeter. (STSCI) Bibliography chaos. (n.d.). Merriam-Webster. Retrieved...
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...The Cohen-Sutherland Algorithm In this algorithm we divide the line clipping process into two phases: (1) identify those lines which intersect the clipping window and so need to be clipped and (2) perform the clipping. All lines fall into one of the following clipping categories: 1. Visible---both endpoints of the line lie within the window. 2. Not visible---the line definitely lies outside the window. This will occur if the line from (x1, y1) to (x2, y2) satisfies anyone of the following four inequalities: x1, x2 >xmax y1, y2 >ymax x1, x2 <xmin y1, y2 <ymin 3. Clipping candidate--- the line is in neither category 1 nor 2. Midpoint Subdivision An alternative way to process a line in category 3 is based on binary search. The line is divided at its midpoint into two shorter line segments. The clipping categories of the two new line segments are then determined by their region codes. Each segment in category 3 is divided again into shorter segment and categorized. This bisection and categorization process continues until each line segment that spans across a window boundary (hence encompasses an intersection point) reaches a threshold for line size and all other segements are either in category 1 (visible) or in category 2 (invisible). The midpoint coordinates (xm , ym) of a line joining (x1 , y1) and (x2, y2) are given by xm=x1+x22 ym=y1+y22 The Liang-Barsky algorithm for finding the visible portion of the line, if any, can...
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...made by separated software dependent of hardware (interface boxes, oscilloscopes, serial port devices). This software stores its files in a special format “.rw3” that can be only read with Regressi. Regressi is both a spreadsheet and a chart builder that replaced Excel in our High school’ Labs. For instance, this processing software can model a particular experimental curve, trace velocity vectors, derive functions, etc. It also allows comparing diverse set of data from the same experiment and finding highlights the influence of parameters. It can be applied to signal processing, chemistry or mechanics. The aim is to be able to keep record of data collected from experiments, to present it on a graph, and also to apply some ready function to it (such as curve fitting). In the example above, as part of a physics tutorial, we want to represent the graph of the voltage of a capacitor in function of time. We acquire data thanks to an interface Orphy connected to the computer; then, the software Orphy GTS2 gathers the data before we can transfer it to Regressi. Once on Regressi, we can also edit the curves by fitting them, adding tangents, finding values, etc. Therefore, it allows us to entirely exploit the information we collected. It also allows us to present our results in a better shape by changing the colors of the graph, merge graphs or add some text on it (see the legends in the picture above). The bad side about this software is that it requires a lot of practice. Indeed...
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...User’s Guide For fx-9860G Series/GRAPH 75/85/95 Series CASIO Worldwide Education Website http://edu.casio.com CASIO EDUCATIONAL FORUM http://edu.casio.com/forum/ = Page 1 = 20060601 Contents Contents 1 Geometry Mode Overview 2 Drawing and Editing Objects 3 Controlling the Appearance of the Geometry Window 4 Using Text and Labels in a Screen Image 5 Using the Measurement Box 6 Working with Animations 7 Error Messages = Page 2 = 20060601 1-1 Geometry Mode Overview 1. Geometry Mode Overview The Geometry Mode allows you to draw and analyze geometric objects. You can draw a triangle and specify values to change the size of its sides so they are 3:4:5, and then check the measurement of each of its angles. You can also lock the coordinates of a point or the length of a line segment, and you can draw a circle and then draw a line that is tangent to a particular point on the circle. The Geometry Mode also includes an animation feature that lets you watch how an object changes in accordance with conditions you define. Geometry Mode Menus Unlike other modes, the Geometry Mode does not have function menus along the bottom of the screen. Instead, it uses menus named [F1] through [F6] and [OPT], like the ones shown below. The following is a general explanation of Geometry Mode menus. • Pressing a key that corresponds to a menu ([F1] through [F6] or [OPT]) will display the Pressing...
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...at 2 m/s because the velocity does not change because of the consistent speed of the man walking to the house. Since the velocity is constant the acceleration is zero. On the Acceleration-Time graph, the line is flat and straight across at the 0 m/s line because the man does not accelerate. He just walks at a consistent pace to the house. This is called constant speed because there is no variation in his speed. * On the second example, the man is sleeping then wakes up and runs toward the house constantly speeding up as he goes. On the Position-Time graph, there is a positive upward curved line. This is because both are moving in a positive direction but because he is running, the position is rising faster than the time. This upward curve indicates an increase in velocity. On the Velocity-time graph, the line is a straight consistent rise. This is caused because the man is running so the velocity is rising throughout the graph, as is the position. A positive slope indicates a changing velocity which is a positive acceleration. On the Acceleration-Time graph, the line constantly rising because the man is running, constantly speeding up. * On the third example, the man steps outside and walks quickly for 3 meters then he immediately slows down and walks the rest of the way. On the Position-Time graph, the line spikes down quickly then continues in a downward consistent decline. This is because he ran for the first 3 meters then walked at a consistent speed. The reason it...
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...Term Paper Mathematics NAME: BIPIN SHARMA ROLL NO: B59 SECTION: C1903 Conics Conic sections are the curves which result from the intersection of a plane with a cone. These curves were studied and revered by the ancient Greeks, and were written about extensively by both Euclid and Appolonius. They remain important today, partly for their many and diverse applications. Although to most people the word “cone” conjures up an image of a solid figure with a round base and a pointed top, to a mathematician a cone is a surface, one which is obtained in a very precise way. Imagine a vertical line, and a second line intersecting it at some angle f (phi). We will call the vertical line the axis, and the second line the generator. The angle f between them is called the vertex angle. Now imagine grasping the axis between thumb and forefinger on either side of its point of intersection with the generator, and twirling it. The generator will sweep out a surface, as shown in the diagram. It is this surface which we call a cone. Notice that a cone has an upper half and a lower half (called the nappes), and that these are joined at a single point, called the vertex. Notice also that the nappes extend indefinitely far both upwards and downwards. A cone is thus completely determined by its vertex angle. Now, in intersecting a flat plane with a cone, we have three choices, depending on the angle the plane makes to the vertical axis of the cone. First, we may...
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...Line Art Tutorial Recommended for Intermediate Level Photoshop Users First up I’d like to ease your mind and let you know that you don’t need to know how to draw to complete this tutorial. It’s basically tracing, except that tracing is alot easier in Adobe Photoshop. Creating line art with this technique will take several hours to do a good job…if you want a tutorial that just applies a couple of filters, then this tutorial is not for you! You will need to know how to use the PEN TOOL for this tutorial. (If you don’t know how to use the pen tool complete the fast tutorial found HERE first). I suggest you read through the entire tutorial first, before you begin. 1. Preparing the Layers Open your photo in Photoshop. Rename the layer “original”. If your picture is quite dark you will need to lighten it a little. The reason for this is that we will be tracing over the photo in black so we need to be able to see the lines we are creating clearly. Adjust the Brighness of the photo Image >> Adjustments >> Brightness/Contrast… Duplicate the “original” layer. Rename this new layer “top”. Create two more new layers. Place them under the “top” layer. Fill the layer closest to the “original” layer white and rename it “background”. Leave the other layer transparent and rename it “line art” Turn the visibility OFF for the “background” and “top” layers.< Visibility ON for the “line art” and “original” layers and the “line art” layer is active. See image below...
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...one from z = 0 to z = i and other from z = i to z = i+1. b) If f(z) = z2 and C is the line segment from z = 0 to z = 2+ i c) If f(z) = z2 and C consists of two line segments, one from z = 0 to z = 2 and other from z = 2 to z = 2+i. d) If f(z) = 3z + 1 and C follows the figure e) If [pic] , C is a circle [pic]and [pic] f) If [pic] and the path of integration C is the upper half of the circle [pic] from z = -1 to z = 1. g) If [pic] and C is 1) the semicircle [pic] 2) the semicircle [pic] 3) the circle [pic] h) If [pic] and C is the arc from z = -1 - i to z = 1 + i along the curve [pic]. i) If [pic] and C is the curve from z = 0 to z = 4+2i given by [pic]. j) Evaluate [pic] along: a) The parabola [pic] [pic] b) Straight line from (0, 3) to (2, 3) and then from (2, 3) to (2, 4) c) A straight line from (0, 3) to (2, 4). EXERCISE-05 1. State Cauchy-Goursat theorem . 2. Verify Cauchy-Goursat theorem for the function [pic], if C is the circle [pic] (b) the circle [pic]. 3. State the Cauchy’s integral formula and Cauchy Residue Theorem. 4. Evaluate by Cauchy’s integral formulae and by Residue theorem (a) [pic] (b) [pic] (c) [pic] (d) [pic] (e)...
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...DQ 1. The difference between a scatter plot and a line graph is that scatter plots and line graphs have similarities in that they both use an X-Y axis. But a line graph has a line or curve to describe a formula like Y=2X+5, a Scatter plot is a collection of X-Y coordinates that have no real formula due to real life uncertainties (heinsberg), but, once plotted, can provide a clue to a single formula. On a line graph, the points are connected by a line. Hence the name “line graph”. A scatter plot can be used as an initial record of discrete data values. The range determines a number line, which is then plotted with X’s for each data value. Both kind of plots are useful but it depends on the need. In case of statistical data analysis “scatter plots” may be preferred and for plotting mathematical law or equation “line plot” will be preferred more. DQ 2. If a line has no y-intercept is a vertical line. A line that has no x-intercept is a horizontal line. A line that does not have a y intercept means that does not cross the y-axis. The only way that happens is if the line is a vertical line that is not the y-axis itself. Same idea for x intercept. Except that means the line is a horizontal line that is not the x-axis itself. For example, a graph of cost versus chicken wings eaten. Cost goes up as more chicken wings are eaten. If the same cost was plotted versus chicken wings at an all you can eat buffet, the graph would be a horizontal line. A real world example of a line with...
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...Lashay Snow ECE 301 Homework 8 Developmental Domain: Small motor: cuts out shapes with curved tines; cuts out shapes with straight line. Devin is at the art table working with a small paper sack, scissors, and markers. He is looking at his project and standing as he cuts a straight line in the sack, then cuts another straight line about3 inches lower than the first. He cuts off the ends of the sack, then picks up the cut piece and measures it around his eyes. Next, he takes the scissors and pokes a hole in the sack and cuts a curved, almost round circle doing the same process an inch or so away from the first. He picks up his new creation and puts it around his eyes. He takes it off and, using the scissors, cuts bigger holes. Again, he measures the placement around his eyes, which is still not in the right spot. He looks around the room and soon puts the mask down and walks around and around the table. Devin appeared to be very interested in making a mask for his eyes. He is focusing on the product because he seemed to have a plan for his mask, even cutting with the scissors (starting off with a poke for the eye holes); however, he then got frustrated because he couldn’t get the holes in the right spots for his eyes. He was willing to work with it a short time, but then gives up his project. He executes his plan without prompting. The plan for the mask is a conscious effort, but he does have occasional error with placement and roundness of the curved lines. The...
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...original article by Dapena on this subject was in issue #131 of Track Coach. From this I gather elite jumpers have an unusual sense of finding the right spot to jump from. No matter what the differences are ... they get the runup to work. It is similar to Finnish javelin throwers, who may differ in the first part of the run, but who all seem to know what to do in the last two steps. The path of the footprints in a high jump runup can be idealized as a straight line perpendicular to the bar, followed by a circular arc which ends at the takeoff (Figure I). Such a path is de fined by the position of the takeoff foot (its x and y coordinates), the angle between the bar and the final direction of the footprints' path (f), and the radius of the curve (r). A method for drawing the path of the footprints on the ground was described in previous papers. (See Dapena, et aI., 1993; Dapena, 1995a.) However, the numerical values needed for the implementation of this method were based on limited information. Recent work by Iiboshi, et al. (1994) provides data that can help us to improve the design of the runup. They used a special video analysis technique to measure the footprint locations of the top eight men and seven of the top eight women in the high jump finals of the 1991 World Championships. The last successful jump was analyzed for each athlete, with the exception of Heike Henkel, who had to be studied in a successful jump in which the bar was set 5cm below her winning height. The...
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