Task 3
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The document discusses geometric theory and modeling. It explains that the Cartesian coordinate system specifies points using numerical distances from perpendicular lines. Basic modeling uses vertices connected by edges to form triangles as the simplest polygon faces. Modeling programs include primitive objects like cubes, pyramids and cylinders that can be edited by resizing or reshaping. Polygons can be given surfaces like textures and colors to define models, such as adding armor textures to parts of an alien character.
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Geometry theory
3D computer graphics employ the same principles as 2D vector artwork but with an additional axis. The basic objects used in 3D mesh modeling are vertices (points in 3D space) and edges (lines connecting two vertices). Polygons like triangles and quads are formed from edges and vertices and are the most common shapes used in polygonal modeling. A group of connected polygons sharing vertices is referred to as a mesh or wireframe model.
Geometric theory task 3 3 d the basics
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describes the geometry when the used cameras are calibrated, and the fundamental matrix expresses the
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estimate the fundamental matrix. Although it is a landmark of computer vision, in the current work, three
derivations of the essential and fundamental matrices have been revised. The Longuet-Higgins' derivation
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2. The working coordinate system (WCS) is user-defined to facilitate geometric construction.
3. The screen coordinate system (SCS) is device-dependent with its origin at the lower left display corner.
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Human eyes perceive 3D projections in 2D. Coordinate systems including 1D, 2D, and 3D Cartesian systems define locations using reference points and orthogonal axes. 3D systems use x, y, and z coordinates to locate points and define geometries in space, including volumes like cubes and spheres. Coordinate transformations allow changing between reference frames.
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describes the geometry when the used cameras are calibrated, and the fundamental matrix expresses the
geometry when the cameras are uncalibrated. Since the nineties, researchers devoted a lot of effort to
estimate the fundamental matrix. Although it is a landmark of computer vision, in the current work, three
derivations of the essential and fundamental matrices have been revised. The Longuet-Higgins' derivation
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The document discusses cross sections of 3D figures. It explains that when a 3D figure like a cube or sphere is cut in half, the cross section forms a 2D shape like a square or circle. For a cone with a radius of 8cm and height of 13cm, the cross section cut through the center forms a triangle with a base of 16cm, the diameter of the circle, and a height of 13cm. The area of the triangle is calculated as 104cm2.
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This document discusses various metric relationships in mathematics including proofs, congruency, similarity, angles, triangles, and the Pythagorean theorem. It defines key concepts such as complementary angles, supplementary angles, opposite angles, interior angles, corresponding angles, and more. Examples of exam questions are provided testing these concepts along with activities for further practice.
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1) Some crop circle patterns resemble geometric shapes called stereoisomers and enantiomers.
2) One crop circle pattern is an enantiomer shape that can be visualized through a 360 degree rotation, representing a 2D slice of a 3D volume containing interior compartments.
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Similar to Task 3
Task 3
Geometric theory uses 3D lighting tricks that employ an extra axis compared to 2D design. Basic objects in mesh modeling include vertices and polygons formed by connecting vertices with edges. Triangles made of three connected vertices are the simplest 2D figures. Surfaces of connected polygons with shared vertices are called meshes, also known as wireframe models, which are useful for simulating light transport in ray tracing.
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This document provides information about axis systems that are important in civil engineering. It discusses how global and local axis systems are used to analyze structural members. A major axis is defined as being parallel to the longest dimension of a member, while minor axes are perpendicular to the major axis. Cross-sections are defined as cuts perpendicular to the major axis. Forces like shear and axial forces are determined based on their direction relative to the major axis. Moment of inertia calculations depend on the axis used. Mohr's circle, which relates stresses, also relies on defining an axis system. Axis systems are thus a fundamental concept in engineering mechanics and the analysis of structures.
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CO-ORDINATE GEOMETRY
Coordinate geometry is a system that describes the position of points on a plane using ordered pairs of numbers. Rene Descartes developed this branch of mathematics in the 17th century. A coordinate plane has two perpendicular axes (x and y) that intersect at the origin point (0,0). The distance between any two points on the plane can be calculated using the Pythagorean theorem. Key concepts covered include finding the midpoint and points of trisection on a line segment, as well as using the section formula to determine the coordinates of a centroid.
COORDINATE GEOMETRY
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This document proposes an algorithm to interpret line drawings of imaginary objects drawn over photographs of an existing scene. The algorithm leverages multi-view stereo reconstruction of the real scene to identify dominant orientations, which it then uses as context to disambiguate the 3D interpretation of the line drawing. It formulates the problem as a labeling task that assigns orientations to each facet of the drawing, favoring orientations from the existing scene structure over new orientations. The algorithm is demonstrated on tasks in architecture, furniture design, and cultural heritage.
11. Define a simple deformable model to detect a half-circular shape.pdf
11. Define a simple deformable model to detect a half-circular shape (may be rotated). What will
be the energy function?
Solution
shape is a recurring theme in computer vision. For example, shape is one of the main sources of
information that can be used for object recognition. In medical image analysis, geometrical
models of anatomical structures play an important role in automatic tissue segmentation. The
shape of an organ can also be used to diagnose diseases. In a completely different setting, shape
plays an important role in the perception of optical illusions (we tend to see particular shapes)
and this can be used to explain how our visual system interprets the ambiguous and incomplete
information available in an image. Our main goal is to develop techniques that can be used to
represent and detect relatively generic objects in images. The techniques we present here revolve
around a particular shape representation, based on the description of objects using triangulated
polygons. Triangulated polygons allow us to describe complex shapes using simple building
blocks. As we show in the next section, the triangles that decompose a polygon without holes are
connected together in a tree structure, and this has important algorithmic consequences. By
picking a particular triangulation for the polygons we obtain decompositions of objects into
meaningful parts. This yields a discrete representation closely related to Blum’s medial axis
transform [6]. In this paper we concentrate on the task of finding the location of a deformable
shape in an image. This problem is important for the recognition of non-rigid objects. Moreover,
objects in many generic classes can be described as deformed versions of an ideal template. In
this setting, the location of an object is given by a continuous map from a template to an image.
Figure 1 illustrates how we use a deformable template to detect a particular anatomical structure
in an MR image. We will show how triangulated polygons provide rich models for deformable
shapes. These models can capture both boundary and interior information of an object and can be
deformed in an intuitive way. Equally important, we present an efficient algorithm for finding
the optimal location of a deformable shape in an image. In contrast, previous methods that take
into account the interior of deformable objects.
The geometric properties of rigid objects are well understood. We know how three dimensional
features such as corners or edges project into images, and there are a number of methods that can
be used to represent rigid shapes and locate their projections. Some techniques, such as the
alignment method [23], use explicit three dimensional representations. Other techniques, such as
linear combination of views [36], capture the appearance of three dimensional shapes using a
small number of two dimensional pictures. These and similar techniques assume that all shape
variation comes from the viewpoint dependency of two dimensiona.
Photogrammetry1
Photogrammetry is a technique for measuring objects using photographs without touching them. It involves taking photographs from different positions and using triangulation to determine the three-dimensional coordinates of points on the objects. The main principle is triangulation, which allows lines of sight from camera positions to be intersected to calculate 3D coordinates. Photogrammetry has been used since the 1850s and has evolved with improvements in computing power to allow digital photogrammetry techniques. It can be used for close-range terrestrial applications or long-range aerial applications.
Eucluidian and Non eucluidian space in Tensor analysis.Non Euclidian space
The document discusses Euclidean geometry and how it differs from non-Euclidean geometry. In Euclidean geometry, objects can be moved without deformation, compared using congruence and similarity, and parallel lines never meet. Non-Euclidean geometry describes spaces like spheres where parallel lines intersect and the sum of angles in a triangle is greater than 180 degrees. The document also introduces different coordinate systems used to describe geometric spaces, including Cartesian, cylindrical, and spherical coordinate systems. It discusses the properties of vectors in these systems and the concepts of covariant and contravariant vectors.
posterfinal
This document describes a method for 3D reconstruction from a single image using single-view metrology. Key steps include detecting vanishing points to establish directions in the scene, calculating planar homographies to map image points to world coordinates, and using metric constraints to estimate distances and reconstruct occluded objects. Examples demonstrate reconstructing buildings and objects from single images. Limitations include reliance on planar surfaces and regular object shapes.
0000556
The document describes algorithms for reconstructing curved solids from two polygonal orthographic views. It presents methods for first reconstructing all possible polyhedral solids that correspond to the two views, and then modifying the generated third views to include circular arcs, allowing for solids bounded by quadric surfaces. The key steps are to analyze line and vertex multiplicities in the views to identify ambiguities, reconstruct all valid polyhedral solids, and then reason about replacing line segments with curves in the generated third views. The algorithms ensure completeness by considering all valid configurations of faces during the reconstruction process.
Vskills Certified CAD Sample Material
This document provides an introduction to computer-aided design (CAD) including basics of CAD systems and geometric elements used in CAD. It discusses how CAD is used to design curves, figures and objects in both 2D and 3D space. It also summarizes different types of CAD systems and applications, as well as coordinate systems and how points are represented in Cartesian and polar coordinate systems in CAD.
coordinates system
This document discusses the five main types of coordinate systems: Cartesian, polar, cylindrical, spherical, and curvilinear. It provides details on the definition and key aspects of each system. The Cartesian system is attributed to René Descartes and uses perpendicular x and y axes. The polar system specifies points using an angle and distance from a central point. Cylindrical coordinates use distance from an axis, angle from a reference direction, and distance from a plane. Spherical coordinates rely on radial distance and two angular measurements. Curvilinear coordinates involve curved coordinate lines rather than straight ones.
A resource for Interdisciplinary Learning
Coordinate geometry uses a system of x and y coordinates to determine the exact location of points on a plane. It has many applications, including calculating distances and sizes of shapes, defining locations using latitude and longitude, air traffic control, map projections, computer graphics, robotics, and art. Geometry underlies key technologies like GPS, digital files, video games, and more.
Analytical geometry
Okay, here are the steps to solve this problem:
1) The sphere has a radius of 8 inches
2) To find the volume of a sphere we use the formula: V = (4/3)πr^3
3) Plugging in the values:
V = (4/3)π(8)^3
V = (4/3)π(512)
V = 1024π
So the volume of the spherical fish tank with a radius of 8 inches is 1024π cubic inches.
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The document discusses different types of production briefs that could be used for creating media products for clients. It provides examples of briefs for competitions, including briefs for creating games for Armor Games, games for Steam Greenlight, and games for reviews on IGN. For each competition example, it outlines the client, required product, timescale, target audience, legal/ethical considerations, and constraints. The document serves to illustrate how production briefs provide guidance and set expectations for creating media products for different clients and platforms.
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Production log
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This document contains a production diary for a 3D animation project. It summarizes the progress made each week from April to June, including research, storyboarding, modeling, texturing, rigging, and animation. The student's plan for the following week is also provided each time, with the goal of completing all animation sequences and rendering the final product by mid-June.
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- 2. The Cartesian coordinate system is a system that specifies each point uniquely in a plane by a pair of numerical coordinates that are signified distances from the point to two fixed perpendicular lines which are measured to the same length. CARTESIAN COORDINATE SYSTEM http://upload.wikimedia.org/wikipedia/commons/0/0e/Cartesian-coordinate- system.svg
- 3. A basic object is used in mesh modelling this is called vertex and when two vertices are supported by a straight line and this becomes an edge, and when three vertices are connect to one another show the shape of a triangle which is the simplest polygon that can be created when modelling and in this case would be a face. GEOMETRIC THEORY AND POLYGONS http://www.webreference.com/3d/cararra/3.html
- 4. In 3D modelling program this is normally pre made objects there for you to construct your own models which consist of a variety of shapes the most simplest would most likely be a cube, pyramid and cylinder. All these primitive objects when created can be edited by either stretching the size of the shape or disfiguring the original shape of the object. PRIMITIVES http://www.webreference.com/3d/cararra/3.html
- 5. Polygons can be given specific surfaces which defines the actual of your model if you were making some form of character, you would most likely do this by adding a certain texture and colour the example to the right hand side shows armour being split into parts which will then be added to this alien looking model. SURFACES http://moon245.3dtotal.com/admin/new_cropper/tutorial_content_images/1769_tid_ 07-02.jpg