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This lesson discusses how to implement diffuse reflection of light.
My solutions works with a grid of four polygons, each providing a possible start or end point for the values 0-90° resp. 0-100%, 90-180° resp. 0-100% and so on, sharing the center point and hence, there are two times 4 segements. You could think about the mechanics as a telescope rod with multiple segments, each doing its segmented job from 0. Imagine a robotic turtle starting at (0, 0) in the x-y plane. After an import turtle, give it the command turtle.forward(15), and it moves (on-screen!) 15 pixels in the direction it is facing, drawing a line as it moves. Give it the command turtle.right(25), and it rotates in-place 25 degrees clockwise.
A Simple Diffuse Lighting Model¶
Light that directly strikes an object and then reflects in all directions iscalled “diffuse” light. The amount of light reflection is determined by theangle between the light ray and the surface normal vector. In Physics,Lambert’s cosine law provides an equation for calculating diffuse color.
The Math for Diffuse Reflection¶
To perform diffuse lighting calculations each vertex that defines a trianglemust have an associated normal vector. The normal vector defines a directionthat is projecting out from the front side of the triangle. The normal vectordefines how light will reflect off of a surface defined at the vertex. Thenormal vector may be 90 degrees to the surface of the triangle, or it might beat some other angle to simulate a curved surface.
The diagram to the right labels the pieces needed to calculate diffusereflection. We need to calculate the angle between the vertex’s normal vectorand a vector pointing at the light source from the vertex. This angleis labeled “theta” in the diagram.
The dot product of two vectors is defined as the sum of the products of theirassociated terms. 3D vectors are normally stored as arrays, where (v[0], v[1], v[2])is the <dx, dy, dz> values of the vector. Therefore, the dot product of vectors v0 and v1 is:
It can be shown that the dot product of two vectors is equal to the cosineof the angle between the two vectors divided by the length of the two vectors.In code format, this means that:
If both v0 and v1 are normal vectors that have a length of 1, the dot productgives the cosine of the angle without any division.
Examine the plot of a cosine curve to the right. Notice that when the angleis zero, the cosine of zero is 1.0. As the angle increases, the cosine of the anglecurves to zero. When the angle is 90 degrees, the cosine of 90 is 0.0.This is lambert’s cosine law. The cosine values are treated as percentages of color.When the angle is zero, cos(0) is 1.0, and you get 100% color. When the angleis 90 degrees, cos(90) is zero and youget 0% color. When the angle becomes greater than 90 or less than -90 the cosinegoes negative. This is an indication that the front side of the triangleis pointing away from the light source. You can’t have a negative percentageof light, so we clamp the cosine of the angle to values between 0.0 and 1.0.
A WebGL Demo Program for Diffuse Lighting¶
Experiment with the following WebGL program. Move the light source andexamine how the colors on the model change.
Manipulate the position of a light source and a camera.
The left canvas shows the relative location of the light source, the camera,and an object. The right canvas shows the scene from the camera's vantage point with the light sourceused to calculate diffuse reflection.
Manipulate the camera's location and center of view:
Manipulate the light's location:
eye (0.0, 0.0, 5.0)
center (0.0, 0.0, 0.0)
light (3.0, 3.0, 3.0)
X: -5.0 +5.0
X: -5.0 +5.0
X: -5.0 +5.0
Y: -5.0 +5.0
Y: -5.0 +5.0
Y: -5.0 +5.0
Z: -5.0 +5.0
Z: -5.0 +5.0
Z: -5.0 +5.0
Open this webgl program in a new tab or window
As you experiment with the demonstration program, please make sure youobserve the following characteristics of diffuse reflection.
Moving the camera has no impact on diffuse reflection. The only elementsinvolved in the calculations are the object’s vertices and the locationof the point light source.
If you move the light source close to a particular face, every pixelon the face potentially has a different color. The program iscalculating the diffuse reflection in the fragment shader pixel by pixel.
Notice that some faces that are “blocked” from the lightstill have a bright color.That is, the face should be getting no light because there is an objectbetween it and the light source. However, our simple light model does not accountfor light being blocked by other objects in the scene. And most peoplenever notice that fact!
This lighting model does not account for the distance from the light toa surface. In the real world, the further an object is from a light source,the less light it receives. We will investigate this in later lessons.
Diffuse Reflection in Shader Programs¶
Please study the following shader programs. Then compare the programsto the comments below.
Vertex Shader¶
All calculations in the fragment shader will be done in “camera space,”so the vertex data is transformed by the model and camera transformations,but not the projection transformation.
The shaders are based on three uniform variables:
u_PVM_transforms: a single transformation matrix that containsthe model, view, and projection transforms.
u_VM_transforms: a single transformation matrix that containsthe model and view transforms.
u_Light_position: a single location (x,y,z) that contains the positionof the point light source in “camera space.” (This location has alreadybeen placed in the scene and multiplied by the view transform.)
The location, (x,y,z,1), normal vector, <dx,dy,dz,0>, and color, (red,green,blue,1),of this vertex that will be interpolated between the vertices of theprimitive element. Therefore, we put this data into varyingvariables associated with this vertex.
There are several conversions between 3-component and 4-component values.You need a 4-component value to perform matrix multiplication between a 4x4matrix and a vertex or vector. Notice that a vertex always gets a 4thcomponent of 1.0, while a vector always gets a 4th componentvalue of 0. This is because vertices can be translated, whilevectors have no position and can’t be translated.
Fragment Shader¶
This calculates the angle between a vector to the lightand the vertex’s normal vector.
Shaders implement vector and matrix math, so when you subtract two vec3variables it is creating a vec3 result.
The value of the vertex normal vector is an interpolation of the normals vectorsat the triangle’s vertices. It is easy to show that this interpolatedvector may not have a unit length. Therefore the v_Normal vectormust be normalized for each fragment.
The percentage of color must be between 0% and 100%. Since the cosine functioncan calculate negative values, the percentage values are clamped to valuesbetween 0.0 and 1.0.
The color value is a (red, green, blue, alpha) value. We want to reduce theamount of color but not change the alpha value. That is why the coloris converted into a vec3, scaled by the percentage, and then converted back toa vec4 with the original alpha value unchanged.
Type of Light Source¶
The example WebGL program above was based on a “point light source”. If youhad a different type of light source, such as a sun light source, the shader programswould have to be changed because the definition of your light source wouldchange, but the fundamental math would be the same.
Glossary¶
diffuse reflection
The amount of reflected light off of a surface is a percentage based onthe angle that the light strikes the surface.
Lambert’s cosine law
The relationship between the angle a light ray hits the surface of aface and the amount of color that is reflected can be calculated usinga cosine function.
dot product
A mathematical operation on vectors that calculates the angle between two vectors.
Academic Standards and Grades
Minimum University Requirements
In Good Standing
To be considered a student in good standing, graduate students must
Maintain an overall minimum grade point average (GPA) of 3.00 (on a 4.00 scale) in all courses taken as a graduate student, and
Maintain an overall minimum grade point average (GPA) of 3.00 (on a 4.00 scale) in all courses taken in each of the student’s degree-seeking programs.
No grade of C- or below will be accepted toward a graduate degree. Students must meet the requirements to be in good standing to graduate. All “I” and “M” grades must be cleared for graduation to be certified. Students who fail to maintain good standing may be placed on probation or academically dismissed.
Grade Point Average (GPA)
The GPA is computed by dividing the total number of quality points by the total number of graded (A-F) hours completed. The total quality points are figured by multiplying the number of credits assigned to each course by the quality point value of the grade given. The GPA is truncated to two decimals (3.48) and is not rounded up.
Credit hours for courses with grades of I, IU, M, MU, N, S, U, Q and grades which are preceded by T (Transfer) are subtracted from the total hours attempted before the GPA is calculated. Graduate students are not eligible for grade forgiveness. All grades earned, regardless of course level, will be posted on the transcript. If a student retakes a course, both grades will be used in the determination of the GPA. Courses taken at USF as non-degree-seeking are not computed in the GPA unless the courses are transferred in and applied to the degree requirements. The program and the college must approve such actions.
Grades for transfer credits accepted toward the degree program will not be counted in the GPA unless the coursework in question was taken as a non-degree-seeking student at USF and meets the requirements stated above (see Institution Based Credit/Transfer of Credit section).
Graduate Grading System
Plus/Minus Grading:
Effective fall semester 2000, graduate and undergraduate grades will be assigned quality points in the Grade Point Average (GPA) grading system. The +/- designation must be included in the syllabus provided at the beginning of the course. The use of the +/- grading system is at the discretion of the instructor. The syllabus policy is available in the office of the Provost.
Letter grade = number of grade points
A+
4.00
A
4.00
A-
3.67
B+
3.33
B
3.00
B-
2.67
C+
2.33
C
2.00
C-
1.6
D+
1.33
D
1.00
D-
0.67
F
0.00
FF
Failure due to academic dishonesty1
IA
Incomplete, grade points not applicable
IB
Incomplete, grade points not applicable
IC
Incomplete, grade points not applicable
ID
Incomplete, grade points not applicable
IF
Incomplete, grade points not applicable*
M
Missing grade/no grade reported by instructor, grade points not applicable
MF
Missing grade changed to F, 0.00 grade points
MU
Missing grade changed to U, grade points not applicable
N
Audit, grade points not applicable
S/U
Satisfactory/Unsatisfactory, grade points not applicable
W
Withdrawal or drop from course without penalty, grade points not applicable
Z
Continuing registration in multi-semester internship or Thesis/Dissertation courses, grade points not applicable
*Incomplete grade policy change effective fall 08. IF grades earned and posted prior to fall 2008 do calculate in the GPA; IF grades earned as of fall 2008 forward do not calculate in the GPA Refer to Incomplete Grade Policy for more information.
Satisfactory (S)/ Unsatisfactory (U)
Graduate students may not take courses in the major on an S/U (satisfactory / unsatisfactory) basis unless courses are specifically designated S/U in the Catalog. Students may take courses outside of the major on a S/U basis with prior approval of the course professor, major professor or advisor, and the Dean of the College in which the student is seeking a degree. The student may apply a maximum of six (6) hours of such credit (excluding those courses for which S/U is designated in the Catalog) toward a master’s degree. Daily 1 7 3. Directed Research, Thesis, and Dissertation courses are designated as variable credit and are graded on an S/U basis only. Before a student begins work under Directed Research, a written agreement must be completed between the student and the professor concerned, setting forth in detail the requirements of the course.
Incomplete (I)
Definition: An Incomplete grade (“I”) is exceptional and granted at the instructor’s discretion only when students are unable to complete course requirements due to illness or other circumstances beyond their control. This applies to all gradable courses, including pass/fail (S/U).
Students may only be eligible for an “I” when:
the majority of the student’s work for a course has been completed before the end of the semester
the work that has been completed must be qualitatively satisfactory
the student has requested consideration for an “I” grade as soon as possible but no later than the last day of finals week.
The student must request consideration for an Incomplete grade and obtain an “I” Grade Contract from the instructor of record. Even though the student may meet the eligibility requirements for this grade, the course instructor retains the right to make the final decision on granting a student's request for an Incomplete. The course instructor and student must complete and sign the “I” Grade Contract Form that describes the work to be completed, the date it is due, and the grade the student would earn factoring in a zero for all incomplete assignments. The due date can be negotiated and extended by student/instructor as long as it does not exceed one semester from the original date grades were due for that course.
3.0 Gpa
The instructor must file a copy of the “I” Grade Contract in the department that offered the course and the Graduate School by the date grades are due. The instructor must not require students to either re-register for the course or audit the course in order to complete the “I” grade. Students may register to audit the course, with the instructor’s approval, but cannot re-take the course for credit until the I grade is cleared.
An I grade not cleared within the next academic semester (including summer semester) will revert to the grade noted on the contract. I grades are not computed in the GPA, but the grade noted on the contract will be computed in the GPA, retroactive to the semester the course was taken, if the contract is not fulfilled by the specified date. When the final grade is assigned, if applicable, the student will be placed on academic probation or academically dismissed (refer to Automated Academic Probation Procedures for information). Students cannot be admitted to doctoral candidacy or certified for graduation with an “I” grade.
Example:
• student has a “B” in the course, not including the grade for the missing assignment, therefore is eligible for an “I”
• student’s grade, including a zero for the missed work, would be an “D”
• student and instructor complete the “I” Grade Contract, assigning an “ID” (Incomplete +D grade)
Deadline Agreed Upon in Contract (e.g. two weeks):*
If the student completes the work as agreed upon in the Contract by the noted deadline
Dmg Canvas 3 0 90 Degree Battery Lug
• instructor submits a change of grade
Dmg Canvas 3 0 90 Degree Header
• student earns final grade comprised of all completed course work
If the student does not complete the work as agreed upon in the Contract by the noted deadline
• “I” automatically drops off and the grade of “D” remains.
• GPA is recalculated for the current semester and retroactively recalculated for the semester in which the “I” was granted.
*Although the instructor establishes the deadline for completion of the work, the deadline may only extend through the end of the subsequent semester.
Missing (M)
The University policy is to issue an M grade automatically when the instructor does not submit any grade for a graduate student (undergraduate rules apply to undergraduate and non-degree-seeking students). Until it is removed, the M is not computed in the GPA. An M grade which is not cleared within the next academic semester (including summer semester) will be converted to MF or MU, whichever is appropriate. MF grades are calculated in the GPA and if applicable, the student will be placed on academic probation or academically dismissed. To resolve the missing grade, students receiving an M grade must contact their instructor. If the instructor is not available, the student must contact the instructor’s department chair. Students cannot be admitted to doctoral candidacy or certified for graduation with an M grade.
Continuing Registration Grades (Z)
The Z grade shall be used to indicate continuing registration in multi-semester internship or thesis/dissertation courses where the final grade to be assigned will indicate the complete sequence of courses or satisfactory completion of the thesis/dissertation. Upon satisfactory completion of a multi-semester internship or thesis/dissertation, the final grade assigned will be an S. The Graduate School submits the change of grade for the last registration of thesis/dissertation courses once the thesis/dissertation has been accepted for publication.
Note: Graduation will not be certified until all courses have been satisfactorily completed. No grade changes will be processed after the student has graduated except in the case of university error. Procedures requiring petitions are processed through the Graduate School.
Probation
Any student who is not in good standing at the end of a semester shall be considered on probation as of the following semester. The college or program may also place students on probation for other reasons as designated by the college or program. Notification of probation shall be made to the student in writing by the department, with a copy to the College Dean. At the end of each probationary semester, the department shall recommend, in writing, to the College Dean one of the following:
1. Removal of probation
2. Continued probation; OR
3. Dismissal from the degree program
Students with a GPA below 3.00 for two consecutive semesters will be prevented from registering for courses without the permission of the College Dean. The College Dean will notify the Dean of the Graduate School in cases of academic dismissal. To be readmitted, the student will need to reapply for admission, meeting the admission criteria in place at the time. For information on the Automated Probation Process go to: http://download.grad.usf.edu/Automated_Academic_Probation.pdf
Voluntary Withdrawal
A student may withdraw from the university without grade penalty by the University deadline. Information on the different types of withdrawal (i.e., withdrawing from a single class – see the Drop section, an entire semester, or from the degree program itself) can be obtained from the Registrar’s Office. Appropriate alternative calendar dates may apply. Students who withdraw may not continue to attend classes.
Transfer of Credit
USF has two degree-granting institutions: USF-Tampa (which includes USF Polytechnic and USF Sarasota-Manatee) and USF-St. Petersburg. Students may, with the approval of their graduate program, earn credits at any of the USF institutions. However, the majority of credits needed for a degree must be earned through instruction offered by the institution granting the degree. Students may request a transfer of credit toward their degree program. There are two types of transfer of credit:
Internal Institution Transfer of Credit
Credits earned from USF Tampa, USF Polytechnic, or USF Sarasota-Manatee.
External Institution Transfer of Credit
Credits earned from USF-St. Petersburg or other regionally accredited institutions
Requirements for Transfer of Credit
• Hours: Credits may be transferred as indicated on the appropriate tables below
• GPA: Credits transferred in must have a grade of B or better
• For Internal Institution Credits, the grade of the transferred course(s)
• Are calculated in the GPA at USF
• Are noted on the transcript as the grade earned
• For External Institution Credits, the grade of the transferred course(s)
• Are not calculated in the GPA at USF
• Are noted on the transcript by a N/A if from a USF Regionally accredited institution*
• Evaluation/Approval: The graduate program / department will be responsible for evaluating, approving, and initiating the transfer as soon as possible following admission. • Time Limits: All coursework transferred into a graduate program can be no older than
• seven (7) years at the time of graduation for a master’s and Ed.S. program
• eight (8) years at the time of graduation for a doctoral program.
• There is no time limitation for courses from a completed master’s degree or professional degree used toward a doctoral degree.
• For readmission, refer to the Readmission Policy.
*USF accepts credits from all regionally accredited institutions in the nation.
Up to one graduate course (1 course may be applied to up to 2 certificates)
Up to 12 graduate hours*
Up to 12 graduate hours*
Uncompleted Master’s or Ed.S. Degree
Discretion of the Program
Discretion of the Program
Discretion of the Program
Completed Master’s or Ed.S. Degree
Discretion of the Program
Specific course requirements in common across both degree programs may be waived with the substitution of other approved coursework at the discretion of the program.
Up to 50% of the doctoral program requirement for total course hours (excluding dissertation hours)
Uncompleted Doctoral or completed Professional Degree
Discretion of the Program
Specific course requirements in common across both degree programs may be waived with the substitution of other approved coursework at the discretion of the program.
Up to 50% of the doctoral program requirement for total course hours (excluding dissertation hours)
Completed Doctoral Degree
Discretion of the Program
Specific course requirements in common across both degree programs may be waived with the substitution of other approved coursework at the discretion of the program.
Specific course requirements in common across both degree programs may be waived with the substitution of other approved coursework at the discretion of the program.
*A maximum of twelve (12) internal credits can be transferred to a degree regardless of the source(s) **Programs that wish to transfer credit from a completed doctoral program to a professional program must submit the proposal to the Graduate School for approval.
EXTERNAL INSTITUTION
To Graduate Certificates
To Master’s or Ed.S. Degree
To Doctoral Degree**
Courses (equivalent to 4000 and above) taken as an undergraduate but not applied to undergraduate degrees
Scherlokk 3 5 – find and compare files google drive. Up to one graduate course
Up to 12 graduate hours*
Up to 12 graduate hours*
Completed Certificate
Up to one graduate course
Up to 12 graduate hours*
Up to 12 graduate hours*
Uncompleted Master’s or Ed.S. Degree
Up to one graduate course
Up to 40% of the USF program
Up to 40% of the USF program
Completed Master’s or Ed.S. Degree
Up to one graduate course. Specific course requirements in common across both programs may be waived with the substitution of other coursework at the discretion of the program.
Specific course requirements in common across both degree programs may be waived with the substitution of other approved coursework at the discretion of the program.
Up to 40% of the USF doctoral program requirement for total course hours (excluding dissertation hours)
Uncompleted Doctoral or completed Professional Degree
Up to one graduate course
Up to 40% of the USF program
Up to 40% of the USF doctoral program requirement for total course hours (excluding dissertation hours)
Completed Doctoral Degree
Up to one graduate course. Specific course requirements in common across both programs may be waived with the substitution of other coursework at the discretion of the program.
Specific course requirements in common across both degree programs may be waived with the substitution of other approved coursework at the discretion of the program.
Specific course requirements in common across both degree programs may be waived with the substitution of other approved coursework at the discretion of the program.
*A maximum of twelve (12) credits can be transferred to a degree regardless of the source(s)
**Programs that wish to transfer credit from a completed doctoral program to a professional program must submit the proposal to the Graduate School for approval.
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1Graduate Students who receive an FF will be academically dismissed from the University and will not be eligible to apply to any graduate program at USF. See section on Academic Dishonesty and Graduate School Policy on Academic Integrity for more information.